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

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

Solve for x

$$x=0$$

Steps for Solving Linear Equation

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.

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

Add -1 and 1 to get 0.

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

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

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

To find the opposite of x^{2}-2x+1, find the opposite of each term.

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

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

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

Combine -x and 2x to get x.

$$x-1=-1$$

Add 1 to both sides.

$$x=-1+1$$

Add -1 and 1 to get 0.

$$x=0$$