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

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

Simplifying
(n + -1)(n + 1) = n2 + -1

Reorder the terms:
(-1 + n)(n + 1) = n2 + -1

Reorder the terms:
(-1 + n)(1 + n) = n2 + -1

Multiply (-1 + n) * (1 + n)
(-1(1 + n) + n(1 + n)) = n2 + -1
((1 * -1 + n * -1) + n(1 + n)) = n2 + -1
((-1 + -1n) + n(1 + n)) = n2 + -1
(-1 + -1n + (1 * n + n * n)) = n2 + -1
(-1 + -1n + (1n + n2)) = n2 + -1

Combine like terms: -1n + 1n = 0
(-1 + 0 + n2) = n2 + -1
(-1 + n2) = n2 + -1

Reorder the terms:
-1 + n2 = -1 + n2

Add '1' to each side of the equation.
-1 + 1 + n2 = -1 + 1 + n2

Combine like terms: -1 + 1 = 0
0 + n2 = -1 + 1 + n2
n2 = -1 + 1 + n2

Combine like terms: -1 + 1 = 0
n2 = 0 + n2
n2 = n2

Add '-1n2' to each side of the equation.
n2 + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
0 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

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