How do you solve for x in a(x + c ) = b( x - c )?

$a \left(x + c\right) = b \left(x - c\right)$
$a \cdot x + a \cdot c = b \cdot x - b \cdot c$
$a \cdot x - b \cdot x = - a \cdot c - b \cdot c$
$x \cdot \left(a - b\right) = - c \cdot \left(a + b\right)$
Now if $a - b \ne 0$ then $x = - c \cdot \frac{a + b}{a - b}$