Solve (x-2)^2-x=4(x-2)+x(x-1)-4

$$( x - 2 ) ^ { 2 } - x = 4 ( x - 2 ) + x ( x - 1 ) - 4$$

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}.

$$x^{2}-4x+4-x=4\left(x-2\right)+x\left(x-1\right)-4$$

Combine -4x and -x to get -5x.

$$x^{2}-5x+4=4\left(x-2\right)+x\left(x-1\right)-4$$

Use the distributive property to multiply 4 by x-2.

$$x^{2}-5x+4=4x-8+x\left(x-1\right)-4$$

Use the distributive property to multiply x by x-1.

$$x^{2}-5x+4=4x-8+x^{2}-x-4$$

Combine 4x and -x to get 3x.

$$x^{2}-5x+4=3x-8+x^{2}-4$$

Subtract 4 from -8 to get -12.

$$x^{2}-5x+4=3x-12+x^{2}$$

Subtract 3x from both sides.

$$x^{2}-5x+4-3x=-12+x^{2}$$

Combine -5x and -3x to get -8x.

$$x^{2}-8x+4=-12+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-8x+4-x^{2}=-12$$

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

$$-8x+4=-12$$

Subtract 4 from both sides.

$$-8x=-12-4$$

Subtract 4 from -12 to get -16.

$$-8x=-16$$

Divide both sides by -8.

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

Divide -16 by -8 to get 2.

$$x=2$$