Solve for a 91=-7(3a-1)

$91 = - 7 (3 a - 1)$

Rewrite the equation as $- 7 (3 a - 1) = 91$ .

$- 7 (3 a - 1) = 91$

Divide each term in $- 7 (3 a - 1) = 91$ by $- 7$ and simplify.

Divide each term in $- 7 (3 a - 1) = 91$ by $- 7$ .

$\frac{- 7 (3 a - 1)}{- 7} = \frac{91}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 (3 a - 1)}{- 7} = \frac{91}{- 7}$

Divide $3 a - 1$ by $1$ .

$3 a - 1 = \frac{91}{- 7}$

Simplify the right side.

Divide $91$ by $- 7$ .

$3 a - 1 = - 13$

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

Add $1$ to both sides of the equation.

$3 a = - 13 + 1$

Add $- 13$ and $1$ .

$3 a = - 12$

Divide each term in $3 a = - 12$ by $3$ and simplify.

Divide each term in $3 a = - 12$ by $3$ .

$\frac{3 a}{3} = \frac{- 12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 a}{3} = \frac{- 12}{3}$

Divide $a$ by $1$ .

$a = \frac{- 12}{3}$

Simplify the right side.

Divide $- 12$ by $3$ .

$a = - 4$