Solve (2x-2)(x+2)-x^2-(x-2)(x-4)=4

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

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-2 by x+2 and combine like terms.

$$2x^{2}+2x-4-x^{2}-\left(x-2\right)\left(x-4\right)=4$$

Combine 2x^{2} and -x^{2} to get x^{2}.

$$x^{2}+2x-4-\left(x-2\right)\left(x-4\right)=4$$

Use the distributive property to multiply x-2 by x-4 and combine like terms.

$$x^{2}+2x-4-\left(x^{2}-6x+8\right)=4$$

To find the opposite of x^{2}-6x+8, find the opposite of each term.

$$x^{2}+2x-4-x^{2}+6x-8=4$$

Combine x^{2} and -x^{2} to get 0.

$$2x-4+6x-8=4$$

Combine 2x and 6x to get 8x.

$$8x-4-8=4$$

Subtract 8 from -4 to get -12.

$$8x-12=4$$

Add 12 to both sides.

$$8x=4+12$$

Add 4 and 12 to get 16.

$$8x=16$$

Divide both sides by 8.

$$x=\frac{16}{8}$$

Divide 16 by 8 to get 2.

$$x=2$$