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

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

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

Add $4 r$ to both sides of the equation.

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

Add $12 r$ and $4 r$ .

$- 7 q + 16 r = 3 q$

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

Add $7 q$ to both sides of the equation.

$16 r = 3 q + 7 q$

Add $3 q$ and $7 q$ .

$16 r = 10 q$

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

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

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

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

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

Divide $r$ by $1$ .

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

Simplify the right side.

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

Factor $2$ out of $10 q$ .

$r = \frac{2 (5 q)}{16}$

Cancel the common factors.

Factor $2$ out of $16$ .

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

Cancel the common factor.

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

Rewrite the expression.

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