# How do you solve 5[9-x(x+8)]=5x(1-x)?

Oct 8, 2015

Simplify both sides and then use standard methods to obtain:
$\textcolor{w h i t e}{\text{XXX}} x = 1$

#### Explanation:

$\textcolor{red}{5 \left[9 - x \left(x + 8\right)\right]} = \textcolor{b l u e}{5 x \left(1 - x\right)}$

$\textcolor{red}{5 \left[9 - {x}^{2} - 8 x\right]} = \textcolor{b l u e}{5 x - 5 {x}^{2}}$

$\textcolor{red}{- 5 {x}^{2} - 40 x + 45} = \textcolor{b l u e}{- 5 {x}^{2} + 5 x}$

$\textcolor{w h i t e}{\text{XXX}} - 40 x + 45 = 5 x$

$\textcolor{w h i t e}{\text{XXX}} x = 1$