Solve for q -7q+12r=3q-4r

$- 7 q + 12 r = 3 q - 4 r$

Move all terms containing $q$ to the left side of the equation.

Subtract $3 q$ from both sides of the equation.

$- 7 q + 12 r - 3 q = - 4 r$

Subtract $3 q$ from $- 7 q$ .

$- 10 q + 12 r = - 4 r$

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

Subtract $12 r$ from both sides of the equation.

$- 10 q = - 4 r - 12 r$

Subtract $12 r$ from $- 4 r$ .

$- 10 q = - 16 r$

Divide each term in $- 10 q = - 16 r$ by $- 10$ and simplify.

Divide each term in $- 10 q = - 16 r$ by $- 10$ .

$\frac{- 10 q}{- 10} = \frac{- 16 r}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 q}{- 10} = \frac{- 16 r}{- 10}$

Divide $q$ by $1$ .

$q = \frac{- 16 r}{- 10}$

Simplify the right side.

Cancel the common factor of $- 16$ and $- 10$ .

Factor $- 2$ out of $- 16 r$ .

$q = \frac{- 2 (8 r)}{- 10}$

Cancel the common factors.

Factor $- 2$ out of $- 10$ .

$q = \frac{- 2 (8 r)}{- 2 (5)}$

Cancel the common factor.

$q = \frac{- 2 (8 r)}{- 2 \cdot 5}$

Rewrite the expression.

$q = \frac{8 r}{5}$