# Math Help - Rearranging an equation

1. ## Rearranging an equation

I have the following equation:
t(t - x) = 3y(3y - x)

And I need to rearrange it to find x in the terms of y and t, in simplest form. (Assuming that 3y - t is not equal to 0).

Please could anyone be so kind as to show me how to get to the answer and more importantly, the workings...

I would also be highly appreciative if someone could point me to some online examples...

Thanks in advance, Mez

2. Originally Posted by mezhopking
I have the following equation:
t(t - x) = 3y(3y - x)

And I need to rearrange it to find x in the terms of y and t, in simplest form. (Assuming that 3y - t is not equal to 0).

Please could anyone be so kind as to show me how to get to the answer and more importantly, the workings...

I would also be highly appreciative if someone could point me to some online examples...

Thanks in advance, Mez
$t(t-x)=3y(3y-x)$

Distribute...

$t^2-tx=9y^2-3xy$

Get terms with x on left side, and terms without x on the right side...

$3xy-tx=9y^2-t^2$

Factor out the x on the left side...

$x(3y-t)=9y^2-t^2$

Divide both sides by $(3y-t)$

$x=\frac{9y^2-t^2}{3y-t}$

Factor numerator (difference of squares)

$x=\frac{(3y-t)(3y+t)}{(3y-t)}$

$\boxed{x=3y+t}$

Google "Literal Equations" to find more examples and tutorials.

3. Thank you so much!