(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.