# How do you factor the expression -8x^2 + 24x - 18?

Jun 8, 2018

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

#### Explanation:

$- 8 {x}^{2} + 24 x - 18$

$\therefore - 2 \left(4 {x}^{2} - 12 x + 9\right) = 0$

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

$\therefore 2 x = 3$

$\therefore x = \frac{3}{2}$

Jun 8, 2018

$- 2 {\left(2 x - 3\right)}^{2}$

#### Explanation:

$\text{take out a "color(blue)"common factor } - 2$

$- 2 \left(4 {x}^{2} - 12 x + 9\right)$

$\text{note that "4x^2-12x+9" is a "color(blue)"perfect square}$

$4 {x}^{2} - 12 x + 9 = {\left(2 x - 3\right)}^{2}$

$- 8 {x}^{2} + 24 x - 18 = - 2 {\left(2 x - 3\right)}^{2}$