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

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

Solve for x

$$x=2$$

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}.

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

Use the distributive property to multiply x by x-2.

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

Subtract x^{2} from both sides.

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

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

$$-4x+4=-2x$$

Add 2x to both sides.

$$-4x+4+2x=0$$

Combine -4x and 2x to get -2x.

$$-2x+4=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$-2x=-4$$

Divide both sides by -2.

$$x=\frac{-4}{-2}$$

Divide -4 by -2 to get 2.

$$x=2$$