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

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

Solve for x

$$x=3$$

Steps for Solving Linear Equation

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

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

Consider \left(x+1\right)\left(x-1\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 1.

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

Subtract x^{2} from both sides.

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

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

$$2x-4=-1+x$$

Subtract x from both sides.

$$2x-4-x=-1$$

Combine 2x and -x to get x.

$$x-4=-1$$

Add 4 to both sides.

$$x=-1+4$$

Add -1 and 4 to get 3.

$$x=3$$