# How do you solve for a in v=2(ab+bc+ca)?

$a = \frac{v - b c}{2 \left(b + c\right)}$

#### Explanation:

$v = 2 \left(a b + b c + c a\right)$

$v = 2 a b + 2 b c + 2 c a$

$v = 2 a \left(b + c\right) + b c$

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

$a = \frac{v - b c}{2 \left(b + c\right)}$