Solve for n m+1=-2(n+6)

$m + 1 = - 2 (n + 6)$

Step 1

Rewrite the equation as $- 2 (n + 6) = m + 1$ .

$- 2 (n + 6) = m + 1$

Step 2

Divide each term in $- 2 (n + 6) = m + 1$ by $- 2$ and simplify.

Divide each term in $- 2 (n + 6) = m + 1$ by $- 2$ .

$\frac{- 2 (n + 6)}{- 2} = \frac{m}{- 2} + \frac{1}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 (n + 6)}{- 2} = \frac{m}{- 2} + \frac{1}{- 2}$

Divide $n + 6$ by $1$ .

$n + 6 = \frac{m}{- 2} + \frac{1}{- 2}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$n + 6 = - \frac{m}{2} + \frac{1}{- 2}$

Move the negative in front of the fraction.

$n + 6 = - \frac{m}{2} - \frac{1}{2}$

Step 3

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

Subtract $6$ from both sides of the equation.

$n = - \frac{m}{2} - \frac{1}{2} - 6$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$n = - \frac{m}{2} - \frac{1}{2} - 6 \cdot \frac{2}{2}$

Combine $- 6$ and $\frac{2}{2}$ .

$n = - \frac{m}{2} - \frac{1}{2} + \frac{- 6 \cdot 2}{2}$

Combine the numerators over the common denominator.

$n = - \frac{m}{2} + \frac{- 1 - 6 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 6$ by $2$ .

$n = - \frac{m}{2} + \frac{- 1 - 12}{2}$

Subtract $12$ from $- 1$ .

$n = - \frac{m}{2} + \frac{- 13}{2}$

Move the negative in front of the fraction.

$n = - \frac{m}{2} - \frac{13}{2}$