# How do you solve for a in  sa=2ab+2ac+2bc ?

Feb 26, 2016

$a = \frac{2 b c}{s - 2 b - 2 c}$

#### Explanation:

First, get all the terms with $a$ onto the same side of the equation.

Here, I'll subtract $2 a b$ and $2 a c$ from both sides of the equation so that all the terms with $a$ are on the left-hand side.

$s a - 2 a b - 2 a c = 2 b c$

Factor $a$ from every time on the right hand side.

$a \left(s - 2 b - 2 c\right) = 2 b c$

Divide both sides by $s - 2 b - 2 c$.

$a = \frac{2 b c}{s - 2 b - 2 c}$

This is as simplified as possible. Resist the urge to try to break apart the denominator--that's not allowed.