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

Solution for (x-1)(x+1)=x^2-1 equation:

Simplifying
(x + -1)(x + 1) = x2 + -1

Reorder the terms:
(-1 + x)(x + 1) = x2 + -1

Reorder the terms:
(-1 + x)(1 + x) = x2 + -1

Multiply (-1 + x) * (1 + x)
(-1(1 + x) + x(1 + x)) = x2 + -1
((1 * -1 + x * -1) + x(1 + x)) = x2 + -1
((-1 + -1x) + x(1 + x)) = x2 + -1
(-1 + -1x + (1 * x + x * x)) = x2 + -1
(-1 + -1x + (1x + x2)) = x2 + -1

Combine like terms: -1x + 1x = 0
(-1 + 0 + x2) = x2 + -1
(-1 + x2) = x2 + -1

Reorder the terms:
-1 + x2 = -1 + x2

Add '1' to each side of the equation.
-1 + 1 + x2 = -1 + 1 + x2

Combine like terms: -1 + 1 = 0
0 + x2 = -1 + 1 + x2
x2 = -1 + 1 + x2

Combine like terms: -1 + 1 = 0
x2 = 0 + x2
x2 = x2

Add '-1x2' to each side of the equation.
x2 + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.