Solve for y 2xy+6y=0

$2 x y + 6 y = 0$

Factor $2 y$ out of $2 x y + 6 y$ .

Factor $2 y$ out of $2 x y$ .

$2 y (x) + 6 y = 0$

Factor $2 y$ out of $6 y$ .

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

Factor $2 y$ out of $2 y (x) + 2 y (3)$ .

$2 y (x + 3) = 0$

Divide each term in $2 y (x + 3) = 0$ by $2 (x + 3)$ and simplify.

Divide each term in $2 y (x + 3) = 0$ by $2 (x + 3)$ .

$\frac{2 y (x + 3)}{2 (x + 3)} = \frac{0}{2 (x + 3)}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y (x + 3)}{2 (x + 3)} = \frac{0}{2 (x + 3)}$

Rewrite the expression.

$\frac{y (x + 3)}{x + 3} = \frac{0}{2 (x + 3)}$

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{y (x + 3)}{x + 3} = \frac{0}{2 (x + 3)}$

Divide $y$ by $1$ .

$y = \frac{0}{2 (x + 3)}$

Simplify the right side.

Cancel the common factor of $0$ and $2$ .

Factor $2$ out of $0$ .

$y = \frac{2 (0)}{2 (x + 3)}$

Cancel the common factors.

Cancel the common factor.

$y = \frac{2 \cdot 0}{2 (x + 3)}$

Rewrite the expression.

$y = \frac{0}{x + 3}$

Divide $0$ by $x + 3$ .

$y = 0$