Solve for y 9x+6y=-3 for y

$9 x + 6 y = - 3$ for $y$

Subtract $9 x$ from both sides of the equation.

$6 y = - 3 - 9 x$

Divide each term in $6 y = - 3 - 9 x$ by $6$ and simplify.

Divide each term in $6 y = - 3 - 9 x$ by $6$ .

$\frac{6 y}{6} = \frac{- 3}{6} + \frac{- 9 x}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{- 3}{6} + \frac{- 9 x}{6}$

Divide $y$ by $1$ .

$y = \frac{- 3}{6} + \frac{- 9 x}{6}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 3$ and $6$ .

Factor $3$ out of $- 3$ .

$y = \frac{3 (- 1)}{6} + \frac{- 9 x}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$y = \frac{3 \cdot - 1}{3 \cdot 2} + \frac{- 9 x}{6}$

Cancel the common factor.

$y = \frac{3 \cdot - 1}{3 \cdot 2} + \frac{- 9 x}{6}$

Rewrite the expression.

$y = \frac{- 1}{2} + \frac{- 9 x}{6}$

Move the negative in front of the fraction.

$y = - \frac{1}{2} + \frac{- 9 x}{6}$

Cancel the common factor of $- 9$ and $6$ .

Factor $3$ out of $- 9 x$ .

$y = - \frac{1}{2} + \frac{3 (- 3 x)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$y = - \frac{1}{2} + \frac{3 (- 3 x)}{3 (2)}$

Cancel the common factor.

$y = - \frac{1}{2} + \frac{3 (- 3 x)}{3 \cdot 2}$

Rewrite the expression.

$y = - \frac{1}{2} + \frac{- 3 x}{2}$

Move the negative in front of the fraction.

$y = - \frac{1}{2} - \frac{3 x}{2}$