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

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

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Consider \left(x-2\right)\left(x+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.

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

Subtract x^{2} from both sides.

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

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

$$-4=4x+4$$

Swap sides so that all variable terms are on the left hand side.

$$4x+4=-4$$

Subtract 4 from both sides.

$$4x=-4-4$$

Subtract 4 from -4 to get -8.

$$4x=-8$$

Divide both sides by 4.

$$x=\frac{-8}{4}$$

Divide -8 by 4 to get -2.

$$x=-2$$