Find All Complex Solutions 3(y+9)=12y+13

$3 (y + 9) = 12 y + 13$

Simplify $3 (y + 9)$ .

Rewrite.

$0 + 0 + 3 (y + 9) = 12 y + 13$

Simplify by adding zeros.

$3 (y + 9) = 12 y + 13$

Apply the distributive property.

$3 y + 3 \cdot 9 = 12 y + 13$

Multiply $3$ by $9$ .

$3 y + 27 = 12 y + 13$

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

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

$3 y + 27 - 12 y = 13$

Subtract $12 y$ from $3 y$ .

$- 9 y + 27 = 13$

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

Subtract $27$ from both sides of the equation.

$- 9 y = 13 - 27$

Subtract $27$ from $13$ .

$- 9 y = - 14$

Divide each term in $- 9 y = - 14$ by $- 9$ and simplify.

Divide each term in $- 9 y = - 14$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{- 14}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{- 14}{- 9}$

Divide $y$ by $1$ .

$y = \frac{- 14}{- 9}$

Simplify the right side.

Dividing two negative values results in a positive value.

$y = \frac{14}{9}$