Solve for y x^2+4y=2(3x-6-x)+x^2

$x^{2} + 4 y = 2 (3 x - 6 - x) + x^{2}$

Simplify each term.

Subtract $x$ from $3 x$ .

$x^{2} + 4 y = 2 (2 x - 6) + x^{2}$

Apply the distributive property.

$x^{2} + 4 y = 2 (2 x) + 2 \cdot - 6 + x^{2}$

Multiply $2$ by $2$ .

$x^{2} + 4 y = 4 x + 2 \cdot - 6 + x^{2}$

Multiply $2$ by $- 6$ .

$x^{2} + 4 y = 4 x - 12 + x^{2}$

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

Subtract $x^{2}$ from both sides of the equation.

$4 y = 4 x - 12 + x^{2} - x^{2}$

Combine the opposite terms in $4 x - 12 + x^{2} - x^{2}$ .

Subtract $x^{2}$ from $x^{2}$ .

$4 y = 4 x - 12 + 0$

Add $4 x - 12$ and $0$ .

$4 y = 4 x - 12$

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Divide $- 12$ by $4$ .

$y = x - 3$