# How do you solve 0=4(n-4)-6(n-4) using the distributive property?

Mar 25, 2017

See the entire solution process below:

#### Explanation:

First, multiply each term with each parenthesis by the term outside the parenthesis:

$0 = \textcolor{red}{4} \left(n - 4\right) - \textcolor{b l u e}{6} \left(n - 4\right)$

$0 = \left(\textcolor{red}{4} \times n\right) - \left(\textcolor{red}{4} \times 4\right) - \left(\textcolor{b l u e}{6} \times n\right) - \left(\textcolor{b l u e}{6} \times - 4\right)$

$0 = 4 n - 16 - 6 n - \left(- 24\right)$

$0 = 4 n - 16 - 6 n + 24$

Next, on the right side of the equation, group and combine like terms:

$0 = 4 n - 6 n - 16 + 24$

$0 = \left(4 - 6\right) n + 8$

$0 = - 2 n + 8$

Then, subtract $\textcolor{red}{8}$ from each side of the equation to isolate the $n$ term while keeping the equation balanced:

$0 - \textcolor{red}{8} = - 2 n + 8 - \textcolor{red}{8}$

$- 8 = - 2 n + 0$

$- 8 = - 2 n$

Now, divide each side of the equation by $\textcolor{red}{- 2}$ to solve for $n$ while keeping the equation balanced:

$\frac{- 8}{\textcolor{red}{- 2}} = \frac{- 2 n}{\textcolor{red}{- 2}}$

$4 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}} n}{\cancel{\textcolor{red}{- 2}}}$

$4 = n$

$n = 4$