# How do you solve 3(3u + 2) + 5 = 2(2u - 2) ?

Jan 26, 2017

See the entire solution process below:

#### Explanation:

First, expand the terms within parenthesis on both sides of the equation:

$\left(3 \times 3 u\right) + \left(3 \times 2\right) + 5 = \left(2 \times 2 u\right) - \left(2 \times 2\right)$

$9 u + 6 + 5 = 4 u - 4$

$9 u + 11 = 4 u - 4$

Next, subtract $\textcolor{red}{4 u}$ and $\textcolor{b l u e}{11}$ from each side of the equation to isolate the $u$ term while keeping the equation balanced:

$9 u + 11 - \textcolor{red}{4 u} - \textcolor{b l u e}{11} = 4 u - 4 - \textcolor{red}{4 u} - \textcolor{b l u e}{11}$

$9 u - \textcolor{red}{4 u} + 11 - \textcolor{b l u e}{11} = 4 u - \textcolor{red}{4 u} - 4 - \textcolor{b l u e}{11}$

$\left(9 - 4\right) u + 0 = 0 - 15$

$5 u = - 15$

Now, divide each side of the equation by $\textcolor{red}{5}$ to solve for $u$ while keeping the equation balanced:

$\frac{5 u}{\textcolor{red}{5}} = \frac{- 15}{\textcolor{red}{5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} u}{\cancel{\textcolor{red}{5}}} = - 3$

$u = - 3$