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

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

Solve for x

$$x=0$$

Steps for Solving Linear Equation

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

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$x^{2}+2x=x^{2}-2x+1-1$$

Subtract 1 from 1 to get 0.

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

Subtract x^{2} from both sides.

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

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

$$2x=-2x$$

Add 2x to both sides.

$$2x+2x=0$$

Combine 2x and 2x to get 4x.

$$4x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 4 is not equal to 0, x must be equal to 0.

$$x=0$$