# How do you solve for c in a(c - b) = d?

May 4, 2016

$c = \frac{d}{a} + b$ unless $a = 0$...

#### Explanation:

Case $\boldsymbol{a = 0}$

If $a = 0$ then $a \left(c - b\right) = 0$ regardless of the value of $c$.

Hence:

• If $d = 0$ then any value of $c$ is a solution.
• If $d \ne 0$ then no value of $c$ is a solution.

Case $\boldsymbol{a \ne 0}$

If $a \ne 0$ then we can divide both sides of the equation by $a$ to get:

$c - b = \frac{d}{a}$

Then add $b$ to both sides to find:

$c = \frac{d}{a} + b$