Solve for n -6=15m+9n

$- 6 = 15 m + 9 n$

Step 1

Rewrite the equation as $15 m + 9 n = - 6$ .

$15 m + 9 n = - 6$

Step 2

Subtract $15 m$ from both sides of the equation.

$9 n = - 6 - 15 m$

Step 3

Divide each term in $9 n = - 6 - 15 m$ by $9$ and simplify.

Divide each term in $9 n = - 6 - 15 m$ by $9$ .

$\frac{9 n}{9} = \frac{- 6}{9} + \frac{- 15 m}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 n}{9} = \frac{- 6}{9} + \frac{- 15 m}{9}$

Divide $n$ by $1$ .

$n = \frac{- 6}{9} + \frac{- 15 m}{9}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 6$ and $9$ .

Factor $3$ out of $- 6$ .

$n = \frac{3 (- 2)}{9} + \frac{- 15 m}{9}$

Cancel the common factors.

Factor $3$ out of $9$ .

$n = \frac{3 \cdot - 2}{3 \cdot 3} + \frac{- 15 m}{9}$

Cancel the common factor.

$n = \frac{3 \cdot - 2}{3 \cdot 3} + \frac{- 15 m}{9}$

Rewrite the expression.

$n = \frac{- 2}{3} + \frac{- 15 m}{9}$

Move the negative in front of the fraction.

$n = - \frac{2}{3} + \frac{- 15 m}{9}$

Cancel the common factor of $- 15$ and $9$ .

Factor $3$ out of $- 15 m$ .

$n = - \frac{2}{3} + \frac{3 (- 5 m)}{9}$

Cancel the common factors.

Factor $3$ out of $9$ .

$n = - \frac{2}{3} + \frac{3 (- 5 m)}{3 (3)}$

Cancel the common factor.

$n = - \frac{2}{3} + \frac{3 (- 5 m)}{3 \cdot 3}$

Rewrite the expression.

$n = - \frac{2}{3} + \frac{- 5 m}{3}$

Move the negative in front of the fraction.

$n = - \frac{2}{3} - \frac{5 m}{3}$