Solve for n -86=4+5(3n-3)

$- 86 = 4 + 5 (3 n - 3)$

Rewrite the equation as $4 + 5 (3 n - 3) = - 86$ .

$4 + 5 (3 n - 3) = - 86$

Simplify $4 + 5 (3 n - 3)$ .

Simplify each term.

Apply the distributive property.

$4 + 5 (3 n) + 5 \cdot - 3 = - 86$

Multiply $3$ by $5$ .

$4 + 15 n + 5 \cdot - 3 = - 86$

Multiply $5$ by $- 3$ .

$4 + 15 n - 15 = - 86$

Subtract $15$ from $4$ .

$15 n - 11 = - 86$

Move all terms not containing $n$ to the right side of the equation.

Add $11$ to both sides of the equation.

$15 n = - 86 + 11$

Add $- 86$ and $11$ .

$15 n = - 75$

Divide each term in $15 n = - 75$ by $15$ and simplify.

Divide each term in $15 n = - 75$ by $15$ .

$\frac{15 n}{15} = \frac{- 75}{15}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 n}{15} = \frac{- 75}{15}$

Divide $n$ by $1$ .

$n = \frac{- 75}{15}$

Simplify the right side.

Divide $- 75$ by $15$ .

$n = - 5$