Solve (x-2)^2+3x=x(x+1)

$$( x - 2 ) ^ { 2 } + 3 x = x ( x + 1 )$$

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}.

$$x^{2}-4x+4+3x=x\left(x+1\right)$$

Combine -4x and 3x to get -x.

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

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

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

Subtract x^{2} from both sides.

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

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

$$-x+4=x$$

Subtract x from both sides.

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

Combine -x and -x 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.

$$x=2$$