# How do you solve (2x - 3) ( x - 2) = - 12x + 18?

Nov 1, 2016

$\left(2 x - 3\right) \left(x - 2\right) = - 12 x + 18$

Expand using the foil method.

$2 {x}^{2} - 4 x - 3 x + 6 = - 12 x + 18$

$2 {x}^{2} - 7 x + 6 = - 12 x + 18$

Add $12 x$ and subtract $18$ on both sides...

$2 {x}^{2} - 7 x + 6 + 12 x - 18 = 0$

$2 {x}^{2} + 5 x - 12 = 0$

Factorise...

$\left(2 x - 3\right) \left(x + 4\right) = 0$

When $x = \frac{3}{2}$ and $x = - 4$, what you get is $0$.

$x = \frac{3}{2}$
$x = - 4$