# How do you factor completely bx^2-b = x-b^2x?

May 2, 2018

$x = \frac{1}{b}$ or $x = - b$

#### Explanation:

$b {x}^{2} - b = x - {b}^{2} x$

$\implies b {x}^{2} + {b}^{2} x - x - b = 0$

or $b x \left(x + b\right) - 1 \left(x + b\right) = 0$

or $\left(b x - 1\right) \left(x + b\right) = 0$

i.e. either $b x - 1 = 0$ i.e. $x = \frac{1}{b}$

or $x + b = 0$ i.e. $x = - b$