# How do you solve for v in u(v+2) + w(v-3) = z(v-1)?

Feb 25, 2017

$v = \frac{3 w - z - 2 u}{w - z + u}$

#### Explanation:

Method:

Multiply out the brackets.
All terms with $v$ in on the left. All other terms on the right
Factor out $v$
Rearrange so that $v$ is on its own.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$u v + 2 u + w v - 3 w = z v - z$

$u v + w v - z v = 3 w - z - 2 u$

$v \left(u + w - z\right) = 3 w - z - 2 u$

$v = \frac{3 w - z - 2 u}{w - z + u}$