Solve for y 2(y-3)=2x-6

$2 (y - 3) = 2 x - 6$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y - 3$ by $1$ .

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Divide $- 6$ by $2$ .

$y - 3 = x - 3$

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

Add $3$ to both sides of the equation.

$y = x - 3 + 3$

Combine the opposite terms in $x - 3 + 3$ .

Add $- 3$ and $3$ .

$y = x + 0$

Add $x$ and $0$ .

$y = x$