# How do you solve 42=-6(-3n+6)+6(n-3) using the distributive property?

Jan 5, 2017

To solve this using the distributive property you multiply each term outside a set of parenthesis by each term inside the parenthesis it is associated with. See full explanation of the process below.

#### Explanation:

To solve this using the distributive property you multiply each term outside a set of parenthesis by each term inside the parenthesis it is associated with. We need to pay close attention to the signs of each term.

$42 = \textcolor{red}{- 6} \left(\textcolor{b l u e}{- 3 n} + \textcolor{b l u e}{6}\right) + \textcolor{g r e e n}{6} \left(\textcolor{p u r p \le}{n} - \textcolor{p u r p \le}{3}\right)$

$42 = \left(\textcolor{red}{- 6} \times \textcolor{b l u e}{- 3 n}\right) + \left(\textcolor{red}{- 6} \times \textcolor{b l u e}{6}\right) + \left(\textcolor{g r e e n}{6} \times \textcolor{p u r p \le}{n}\right) + \left(\textcolor{g r e e n}{6} \times \textcolor{p u r p \le}{- 3}\right)$

$42 = 18 n - 36 + 6 n - 18$

We can now group and combine like terms:

$42 = 18 n + 6 n - 36 - 18$

$42 = \left(18 + 6\right) n - 54$

$42 = 24 n - 54$

We can now use normal algebra to solve for $n$:

$42 + \textcolor{red}{54} = 24 n - 54 + \textcolor{red}{54}$

$96 = 24 n - 0$

$96 = 24 n$

$\frac{96}{\textcolor{red}{24}} = \frac{24 n}{\textcolor{red}{24}}$

$4 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{24}}} n}{\cancel{\textcolor{red}{24}}}$

$4 = n$

$n = 4$