Thank you so much!! Cubic equations like "x^3-7x+6" is very rare. Luckily, I found it here so your video helped me a lot. Thanks again LOL!
@suvranilchoudhury6452
3 жыл бұрын
maybe u just didn't focus on maths properly, it isn't at all rare.
@andrii21
3 жыл бұрын
@@suvranilchoudhury6452 Yeah, I am refreshing my knowledge on Math on that time since I am lazy studying Maths when I was at elementary school to half of my Senior High lel.
@suvranilchoudhury6452
3 жыл бұрын
@@andrii21 oh that's great
@kumarvinay5724
3 жыл бұрын
Hi
@minamk3282
3 жыл бұрын
@@andrii21 yes it is super rare ive been looking for a video explaining how to do it and i only found this one
@andrewhealey7698
3 жыл бұрын
I hate to be the one that makes a negative comment but this method does not work. All these examples just happen to be examples where the coefficient's add up to 0 (a+b+c+d=0) so x=1 will always be a solution. this method does NOT work because you could very easily change the leading coefficient to anything other than 1 and the 3rd term ( the 'x' term) to anything other than what is given in the examples and this method will fail outright. This method may look like it "works" for very specific Cubic's but it is not a tool I would recommend learning as it will fail for almost all other Cubic's. For example, try 3x^3 + 11x^2 - 25x + 13=0 . If you follow the same rules given in this video you will get the same factors but you get completely wrong solutions!!
@AlexonHughes
3 ай бұрын
So what method do you use to solve these type of equations ? Just asking because I want to find the universal method for solving all types of cubic equations rather than hit and trial.
@andrewhealey7698
3 ай бұрын
@@AlexonHughes Thanks for replying to my comment. I posted this response such a long time ago I actually forgot about this. LOL.... for me solving any random cubic equation is a pretty specific process. I would start with synthetic division to see if there happens to be an even solution to the equation. so if x=1 or x=2 etc. happens to be a solution then you can factor (x-1) or (x-2) out of the cubic equation and the remaining quadratic can be solved with the quadratic formula. If there are NO even solutions to the equation then you can use the cubic formula (math.vanderbilt.edu/schectex/courses/cubic/) to get at least one solution. But ultimately cubics that don't have at least one even solution can be very cumbersome to deal with...... I don't even want to get into quartics like x^4 powers (major headache!!) LOL
@coolkaw4497
Ай бұрын
@@andrewhealey7698 Thanks for this reply. I'm currently taking Linear Algebra (and have taken calc 1, 2 already) and had no idea how to solve these sorts of cubic equations (I don't recall ever learning this in math 😭). The method in the video just so happened to work with the polynomial I had obtained from trying to calculate the eigenvalues of a 3x3 matrix. I will look into this more reliable method now for future reference!
@andrewhealey7698
Ай бұрын
@@coolkaw4497 That's really cool. I graduated with my math degree back in 2007. To be honest, I was never really taught in any college class how to solve cubic equations either. I was more or less just self taught. and like said, there is really no great cookbook recipe for how to solve cubics. They are relatively straightforward if there happens to be at least 1 whole number solution (i.e x=1, x=2,x=3 etc...) Then you can factor that solution out and you are left with an easy quadratic to solve. Without at least one whole number solution they can be a bit of a headache. But I know one thing the method taught in this youtube video is complete non-sense and will only work for very VERY specific cubics and the creator of this video really does a disservice to anyone trying to learn how to properly solve a cubic equation.
@sakthishridevis998
3 жыл бұрын
I watched around six videos today on solving cubic equations, best one so far. thanks a million!
@PreMath
3 жыл бұрын
Glad to hear that Sakthi! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃 Keep smiling😊
@Jonathan-vx7xi
4 жыл бұрын
simple, elegant...why isn't this being taught as the norm?? thank you
@PreMath
4 жыл бұрын
You are very welcome Jonathan! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep sharing my channel with your family and friends. Take care dear and all the best 😃
@yuvamaths
3 жыл бұрын
Really fantastic method of solving cubic polynomials. Very easy and time saving method too. Thanks a lot for sharing this type of shortcut methods sir.
@bahugunaswarnim
3 жыл бұрын
It's like now every expert mathematics teacher is Indian🥰🥰🥰🥰
@PreMath
3 жыл бұрын
You are awesome my friend! Please keep sharing premath channel with your family and friends. Take care dear and stay blessed😃 Have a very happy and blessed New Year!
@doctorjacksonville7092
2 жыл бұрын
Only works if the product of the two constant in two binomial roots + the sum of the two constant in two binomial roots multiplied to the constant of the third binomial root is equal to the coefficient with the linear variable x. (x + a) (x + b) (x + c) = [a + b] [c] + [a x b] Otherwise, a different answer would pop out, which is most probably irrational or imaginary.
@kailashpandit133
2 жыл бұрын
Right
@SolveMathswithEase
2 жыл бұрын
Try solving this one: kzitem.info/news/bejne/xnxvumeZioR2g6w
@xavier6062
3 жыл бұрын
Sir pls tell in comment section that how to factorize this one through this method Question) x³+3x²+3x-7 Pls tell
@kfjfkeofitorhf9520
Жыл бұрын
X=1 1+3+3-7=0
@ayushpratapsingh2540
3 жыл бұрын
This is the best method of solving cubic equation i found on youtube. Thanks!
@PreMath
3 жыл бұрын
You are very welcome Ayush! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
@timeonly1401
2 жыл бұрын
These cubics all have 1 has a root (since sum of all coefficients = 0). Thx to your channel, a couple others, I always check +/-1 (if sum[coeffs of odd-power terms] = sum[coeffs of even-power terms, then -1 is a root). Using synthetic div to get the quotient quadratic... which can be factored using inspection, grouping, or quadratic formula to get remaining roots.
@waaahhhvishhh9408
Жыл бұрын
Amazing thanks
@sleepeasyguitar9505
6 ай бұрын
This is one of the most helpful methods I've ever learnt. Thank you!
@pranavnarware6366
2 жыл бұрын
before seeing this video , i was also thinking about the relation between constant and any other number , but i also couldn't find the relation. Finally i see your video and understand much better
@janjanboquia6738
Жыл бұрын
does this also apply to cubic polynmials that has leading coefficients greater than one (ax3+bx2.... wer a>1
@arsyanazhima4513
2 жыл бұрын
I've tried this method on different cubic equation and re-multiply them to check whether it's right or wrong and it's not always right. This solving method is too dangerous to be used, it might solve some equation of the cubic factorisation but not all of them. I do not recommend this method. but this is just my opinion on solving cautiously, if you're reckless and a simple person i don't mind. Honestly no offense, rather i respect you "PreMath" for creating such a shortcut, i couldn't done such things.
@bryanjohnson201
6 жыл бұрын
What about when the coefficient for the cubic expression is something other than +1?
@PreMath
6 жыл бұрын
Thank you bryan johnson for this crucial point. I'm in a processing of uploading more vid tutorials that would answer your questions. Please stay tuned. Kind regards
@KaylaMarie_
2 жыл бұрын
ive been looking for this as well. cant find that example anywhere
@thieskersten9084
2 жыл бұрын
It's equal to 0, you can divide everything by the first coefficient. 3x³+9x²+12x-15=0x³+3x³+4x-5=0 Then use the "rational root theorem"
@anuradha9283
Жыл бұрын
What a beauty man i love this method! Waiting to show off to my friends!
@Amansingh_14
3 жыл бұрын
Thank you sir Your video is very helpful for me in solving cubic equations
@JulesMoyaert_photo
8 ай бұрын
I wish I had been taught this method in college!!! SUBSCRIBED!
@ChaniSalvi
8 ай бұрын
I was looking for the Equation 1 kind of questions like how to solve them and yours video helped me..... thanks alot😊😊
@dannykasangili3141
10 ай бұрын
Thank you very much you 've helped me.i didn't know that cubic function is this simple
@user-fy2ud4fq4g
4 ай бұрын
will this work for all degree 3 polynomials? what about x^3-2x^2-x+2=0
@isaaccoleman2960
3 жыл бұрын
YAAAAAS!!!! thankyou so much this an immense help with exams around the corner especilly
@PreMath
3 жыл бұрын
You are very welcome Isaac! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
@ritubes8942
3 жыл бұрын
O God unbelievable thanks a lotttttt Finally found exactly relatable vedio♥️♥️🙏🙏💐💐
@PreMath
3 жыл бұрын
Excellent dear Ritu. You are awesome 👍 Take care dear and stay blessed😃 Love and prayers from the USA!
@ritubes8942
3 жыл бұрын
@@PreMath thank you Sir💐
@SamuelLartha-rb1ni
Жыл бұрын
Your the king of math thanks very much i really appreciate cause now i can work polynomials by ma self please continue with the good work
@AkashSharma-fx8cq
3 жыл бұрын
This is really best method to quickly and easily solve cubic equations .. thanq vry much sir ❤️
@scmtuk3662
3 ай бұрын
This doesn't always work though. It works with x^3 + 11x^2 - 25x + 13 But what happens if you change the co-efficient of x? This doesn't work with x^3 + 11x^2 - 24x + 13. Expanding the expression (x+a)(x+b)(x+c) gives us x^3 + (x^2)c + (x^2)b + bcx + a(x^2) + acx + abx + abc Factoring this gives us: x^3 + (a+b+c)x^2 + (ab+ac+bc)x + abc So, what we _really_ need, is three numbers that satisfy three conditions. The sum of the three numbers must be the co-efficient of x^2 The product of the three numbers must be the constant. And the sum of all possible product pairs must be the co-efficient of x. Also, unrelated to the above, but: Sometimes, however, you may end up having a situation where the numbers that multiply to give you the constant may involve fractions. For example, 13 can be made from -1, -26 and 1/2 If we take -1, -26 and 1/2 and add these together, we get -53/2 If we then take product pairs, 26, -1/2 and -26/2 then add these together, we get 25/2. Therefore, (x-1)(x-26)(x+(1/2)) would be the solutions to the equation x^3 - (53/2)x^2 + (25/2)x + 13 = 0 To remove those fractions, we could then double this, to get 2x^3 - 53x^2 + 25x + 26 = 0
@HTMreal
Жыл бұрын
sir what shall we do if there is a coefficient with X^3 also is it also workable if X is a fraction: the first equation
@waaahhhvishhh9408
Жыл бұрын
Just remove the fraction but multiplying all the terms in the equation by the denominator of the fraction 😁
@ritikarishi2903
3 жыл бұрын
Thanku sir ji
@mahantyruteekraj5132
4 жыл бұрын
Thanks sir i find this formula very much helpful
@PreMath
4 жыл бұрын
You are very welcome Raj! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep sharing my channel with your family and friends. Take care dear and all the best 😃
@manitrathi5532
8 ай бұрын
X^3-7x+6 is very I found everywhere but I can not found this help me a lot
@harikasomisetti2561
Жыл бұрын
Greetings, In this video you are solving all cubic equations having coefficient of x^3 is 1 i.e., a=1. Can you please explain how to solve if a is not equal to 1 also. Thank you.
@armstrongmwaulusi8473
Жыл бұрын
My question too
@simple_idiot
2 жыл бұрын
Thank you🌹
@krishansaini766
2 жыл бұрын
Really help full video
@tangikinatua9858
4 жыл бұрын
Thank you so much❤. This video helps me a lot.....
@PreMath
4 жыл бұрын
You are very welcome Tangikina! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
@joeynatividad3385
3 жыл бұрын
OMG TYSM NOW IT'S A LOT EASIER FOR ME TO ANSWER NOW
@PreMath
3 жыл бұрын
Glad to hear that JoeyLou! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
@mjoycepalma9333
5 ай бұрын
Thank You :)
@justaracoonchillinginatoilet69
3 жыл бұрын
but what if they dont multiply to make the number at the end of the equation and dont add to make the coefficient of x? im not sure how to solve x^3+x^2+2x-3, please help :(
@tokyo222dp4
2 жыл бұрын
Yes am like you hhhh x^3-6x+7
@moth36
2 жыл бұрын
Thank you very much for this helpful video
@bolimbs
2 жыл бұрын
Thank you for this Sir, big help. I'm now able to give my son a clear explanation. 👍🙏👍
@ranamoh7031
3 жыл бұрын
but sir, when picking the three numbers I can choose different signs and get the same answer but the sign will be different so how can I choose the correct sign
@edwardwang7929
Жыл бұрын
if the sum of coefficients of all terms of a polynomial is zero, then x-1 is a factor of this polynomial.
@goldfing5898
Жыл бұрын
3:00 Sorry, but this method only works if you are certain in advance that all three solutions are real and integer, which is not realistic. In particular, you did not check if the coefficient of the first power matches Vieta's rules, too. For the cubic equation x^3 - 7x + 6 = 0, you must check if the three divisors t1 = -1, t2 = -2, t3 = 3 fulfill the three conditions t1 + t2 + t3 = 0 t1*t2 + t1*t3 + t2*t3 = -7 t1 * t2 * t3 = 6 But you did not check if the second condition is fulfilled! In this case, you were lucky because the second condition is indeed fulfilled, but what if the original equation were x^3 - 8x + 6 = 0 or x^3 - 5x + 6 = 0, just to name a few examples? All these equations have coefficients of 0 for x^2 and 6 as the constant, but different (non-integer!) solutions.
@darkomarkovic3373
2 жыл бұрын
x^3-4x^2+4x+x-2=9 So, we get after transformation, equal solution!
@atulsinghal4256
3 жыл бұрын
Thank u thank u thank million thanks to you sir💚🧡💜❤️💚
@PreMath
3 жыл бұрын
You are very welcome Atul! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and all the best😃
@11alaxmitiwari48
3 жыл бұрын
Thanks alot sir.. sir plz clear my doubt that when there would be a no multiplied with x^3 then what changes do we need to make.
@khanabdul819
Жыл бұрын
Very good explanation. Bravo.
@michelle-cv5tg
Жыл бұрын
the best math yt channel!!!
@jim2376
Жыл бұрын
Very helpful. Well explained.
@Pratyai-l9z
3 жыл бұрын
This trick works only in particular questions not in every question.
@mewingcy
Жыл бұрын
Thank you so much, sir!!
@jayaram9468
2 жыл бұрын
Thank you
@RipunjayDeka
3 жыл бұрын
Thank you very much Sir And please help me to solve it x^3-7x^2+36
@RipunjayDeka
3 жыл бұрын
That means in this format ax^3+bx^2+c=0
@kfjfkeofitorhf9520
Жыл бұрын
X=3 27-63+36= -36+36=9
@bijoysharma1143
3 жыл бұрын
Thank u given nice trick..
@PreMath
3 жыл бұрын
You are very welcome Bijoy Sharma! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
@TomakoDela
3 жыл бұрын
can you write the final factor in binomial form for the first question? thx
@PreMath
3 жыл бұрын
Yes, since the binomial form has two terms. Thanks for asking😀 Take care dear and all the best😃 Have a very happy and blessed New Year!
@ntandoyenkosimkhize1818
2 жыл бұрын
Thank you, finally I got it.
@wisemath1084
3 жыл бұрын
Thank you again for your amazing videos!
@SolveMathswithEase
2 жыл бұрын
Try solving this one: kzitem.info/news/bejne/xnxvumeZioR2g6w
@jaideepsingh7955
3 жыл бұрын
Very nice sir. Sir what if the x^3 term has a coefficient ??
@brawlstars-xh7xf
8 ай бұрын
Did you find your answer? because i have that question too
@vishnupatel6358
3 жыл бұрын
Thanks you sir
@augustadaly6915
Жыл бұрын
An awesome simple method to factor cubic equations❤
@goldfing5898
Жыл бұрын
This to be taken with a grain of salt, since it works only in the rare case that the solutions, or at least one solution, is an integer number. It does no help for the general cubic, although such videos do always suggest...
@Radika4590
4 жыл бұрын
thxxxxxxxxxxxxx. ... so much sir
@PreMath
4 жыл бұрын
You are very welcome Lakhvir ji! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
@archanabparchanabp1285
2 жыл бұрын
Thankyou sir
@AZNBOOM808
4 жыл бұрын
How do you use this method if you're roots are non integers?
@Exonorm27
3 жыл бұрын
It’s actually simple. Generally, you find all the factors of “D” term, then plug those factors into the cubic. If one of those factors let’s the equation to =0, then you have already found a solution. If that doesn’t work, then take all the “D” factors and divide them by the “A” coefficient. Plug those “(Factor-ofD) / A” into the cubic and if any of those let the cubic equation =0, then you have found one of the solutions. From there, you need to convert it from a “x=_____” into “x-_____=0”. Then use polynomial long division or synthetic division to pull out a quadratic. Factor the quadratic if possible. The other method is to just graph the cubic and use graphing technology to solve it lmao.
@virensridhar9985
3 жыл бұрын
This shortcut is wrong. Consider equation x3 + 9x2 - 34x + 24 = 0. Going by this method, you can take the three numbers as 4, 3, 2 as well as -1, -2, 12. So which one will you take?? One one will give the correct answer, the other will give wrong answer
@amazaneone1810
2 жыл бұрын
For equations ax^3 + bx^2 + cx + d where a =/= 0 and (x + w) (x + y) (x + z): b = (w + y + z)/a c = ((wy) + (wz) + (yz))/a d = (wyz)/a If a = 1, then division is not required. So, to determine the correct number set, let's first plug 2, 3, and 4 into the formula for c. (2 x 3) + (2 x 4) + (3 x 4) = 6 + 8 + 12 = 26 26 =/= -34 So, let's plug -2, -1, and 12 into the formula for c. (-2 x -1) + (-2 x 12) + (-1 x 12) = 2 - 24 - 12 = -34 -34 = -34 -1, -2, and 12 are correct. Thus, the solutions are x = 1, x = 2, and x = -12.
@dhanvanthsri484
4 жыл бұрын
Super helped me tnks
@PreMath
4 жыл бұрын
You are very welcome Dhanvanth! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
@chinmoydeka2841
Жыл бұрын
Omg sir u r a life saviour 😍🥰.
@GulshanKumar-zl1ip
3 жыл бұрын
What we will do for high no.like 250 or 70..
@rlssrlss7158
3 жыл бұрын
Sir, could you please solve this equation x^3-3x^2-4x-2=0
@ecetech-lecture9636
3 жыл бұрын
Simply superb,
@wandersgirl132
2 жыл бұрын
Thankyou soo much ❣️
@richaparekh4446
4 жыл бұрын
Thanku soo much Sir!
@PreMath
4 жыл бұрын
You are very welcome Richa Parekh! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep sharing my channel with your family and friends. Take care dear and all the best😃
@richaparekh4446
4 жыл бұрын
@@PreMath Sure sir, i will😃
@tibofordeyn1529
2 жыл бұрын
great method!
@RajeshKumar-rf3et
3 жыл бұрын
Thankuu so much sir
@PreMath
3 жыл бұрын
You are very welcome Rajesh! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and all the best😃 Have a very happy and blessed New Year!
@hahaha-kc4zz
Жыл бұрын
Little confused on the first example, my question is x^3-x-6 and it doesn’t split cleanly
@NamanPaliwal19
6 жыл бұрын
What will happen if equation is x³-x-6=0
@abdeslamelhaddouchi9857
5 жыл бұрын
The solution of thé équation is : (x-2)(x^2+2x+3) = 0 s={2 ; -1+2√2 ; -1-2√2 }
@KeithInModesto
4 жыл бұрын
@@abdeslamelhaddouchi9857 I think you may have mistyped this. It should be: s = {2, -1+i√2, -1-i√2} Whereas if you plug in say (-1+2√2) into f(x) = x³-x-6, you get f(-1+2√2) = -30 + 20√2 [or f(-1+2√2) = 10(-3 + 2√2)]
@RubaschMath
4 жыл бұрын
Naman - you can try my method here: kzitem.info/news/bejne/qWuvn6KHaZOTeKQ
@kfjfkeofitorhf9520
Жыл бұрын
X=2 8-2-6=0 6-6=0
@vivificateurveridique1420
Жыл бұрын
What if we have a number before X cubic?
@jastaj..9634
3 жыл бұрын
Best one i saw on youtube thank u sir❣️
@W81Researcher
3 жыл бұрын
What b - 3ac > 0
@waaahhhvishhh9408
Жыл бұрын
@@W81Researcher nob
@akshayapramodc1046
Жыл бұрын
Hii... Solve... S^3 + 6s^2+ 10s + 9
@dmmuhtar
25 күн бұрын
And what about x^3-4x-1=0
@lovemirlicardo5616
3 жыл бұрын
Shocks, thank you so much❤️
@PreMath
3 жыл бұрын
You are very welcome! I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
@dmmuhtar
25 күн бұрын
Please solve x^3+6x^2-12x+8=0
@vipinsawaria
3 жыл бұрын
2x³+x²-5x+2=0.. can this equation solve by this method.
@kfjfkeofitorhf9520
Жыл бұрын
X=1 2+1-5+2= 3-5+2= -2+2=0
@sanskriti9972
3 жыл бұрын
I need answer for this equation: y^3+3root3y^2-3y-root3
@vanshikarajpal1435
3 жыл бұрын
Finally i understood it!!
@rajeshnandi4417
6 ай бұрын
Can we use this method in board exam sir
@purohitabhilash3070
3 жыл бұрын
How to solve if A is not 1 in Ax^3
@Saffron_Krishna
3 жыл бұрын
Really nice
@jyotiprasadpegu-xd7ul
Жыл бұрын
Easiest way to have factor
@optimisticgirl333
2 жыл бұрын
Tq sir
@a20rahuljawale68
2 жыл бұрын
What if the constant is 0
@goldfing5898
Жыл бұрын
Your video does not take one minute, but more than seven minutes! :-)
@waaahhhvishhh9408
Жыл бұрын
Yes obv cuz he taught us the steps in the process, I can do it in 1 minute or slightly more thanks to his method so go get some help
@goldfing5898
Жыл бұрын
@@waaahhhvishhh9408 Just read my other comment on why his method is incomplete and thus would take even more time. He missed to check whether the sum of pair-wise multiplied divisors matches the -7 coefficient of the first power, too.
@RajeshKumar-rf3et
3 жыл бұрын
Best trick sir
@PreMath
3 жыл бұрын
Thanks dear😀
@shridz_
Жыл бұрын
Doesn't work for 4x³-6x²+1=0
@nishikaperera2988
4 жыл бұрын
Very helpful
@warblerab2955
2 жыл бұрын
That is not going to work in many cubic equations. He was ignoring the number in front of the x(in the first problem that number is 7, in the 2nd that number is -25 and in the third one, the number is 5). He totally ignored those numbers. A change in any one of those numbers, and his solution does not work.
@e-learningwithsomendrasing2565
3 жыл бұрын
Thanku sir
@PreMath
3 жыл бұрын
You are very welcome dear. Take care dear and stay blessed😃
@sakirbavra6143
3 жыл бұрын
solve this => x*3-12x*2+43x-44
@justinmudimbu2107
3 жыл бұрын
What about expressions like 6X^3+11X^2-4X-4😭
@PreMath
3 жыл бұрын
Thanks dear for the visit! You are awesome 👍 Take care dear and stay blessed😃 Kind regard
@kaleemahmad6424
4 жыл бұрын
what about x3_15x+2=0
@RubaschMath
4 жыл бұрын
Kaleem - for your example, try my method: kzitem.info/news/bejne/qWuvn6KHaZOTeKQ
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