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

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

Solve for x

$$x=3$$

Steps for Solving Linear Equation

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

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

Add 4 and 4 to get 8.

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

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.

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

Subtract x^{2} from both sides.

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

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

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

Subtract 8 from both sides.

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

Subtract 8 from -4 to get -12.

$$-4x=-12$$

Divide both sides by -4.

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

Divide -12 by -4 to get 3.

$$x=3$$