Solve for y 2y-6-4x+12=18

$2 y - 6 - 4 x + 12 = 18$

Add $- 6$ and $12$ .

$2 y - 4 x + 6 = 18$

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

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

$2 y + 6 = 18 + 4 x$

Subtract $6$ from both sides of the equation.

$2 y = 18 + 4 x - 6$

Subtract $6$ from $18$ .

$2 y = 4 x + 12$

Divide each term in $2 y = 4 x + 12$ by $2$ and simplify.

Divide each term in $2 y = 4 x + 12$ by $2$ .

$\frac{2 y}{2} = \frac{4 x}{2} + \frac{12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{4 x}{2} + \frac{12}{2}$

Divide $y$ by $1$ .

$y = \frac{4 x}{2} + \frac{12}{2}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 x$ .

$y = \frac{2 (2 x)}{2} + \frac{12}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$y = \frac{2 (2 x)}{2 (1)} + \frac{12}{2}$

Cancel the common factor.

$y = \frac{2 (2 x)}{2 \cdot 1} + \frac{12}{2}$

Rewrite the expression.

$y = \frac{2 x}{1} + \frac{12}{2}$

Divide $2 x$ by $1$ .

$y = 2 x + \frac{12}{2}$

Divide $12$ by $2$ .

$y = 2 x + 6$