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

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

Step 1

Simplify $(x + 6) (x - 2)$ .

Rewrite.

$x^{2} + 4 y = 0 + 0 + (x + 6) (x - 2)$

Simplify by adding zeros.

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

Expand $(x + 6) (x - 2)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $- 2$ to the left of $x$ .

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

Multiply $6$ by $- 2$ .

$x^{2} + 4 y = x^{2} - 2 x + 6 x - 12$

Add $- 2 x$ and $6 x$ .

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

Step 2

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

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

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

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

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

$4 y = 4 x - 12 + 0$

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

$4 y = 4 x - 12$

Step 3

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 $4$ .

$y = x - 3$

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

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