Solve for y 2(x-3)+3y=0

$2 (x - 3) + 3 y = 0$

Simplify each term.

Apply the distributive property.

$2 x + 2 \cdot - 3 + 3 y = 0$

Multiply $2$ by $- 3$ .

$2 x - 6 + 3 y = 0$

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

Subtract $2 x$ from both sides of the equation.

$- 6 + 3 y = - 2 x$

Add $6$ to both sides of the equation.

$3 y = - 2 x + 6$

Divide each term in $3 y = - 2 x + 6$ by $3$ and simplify.

Divide each term in $3 y = - 2 x + 6$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Divide $6$ by $3$ .

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