(x-1)=x^2-1

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

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

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

Remove parenthesis around (-1 + x)
-1 + x = x2 + -1

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

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

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

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

Solving
x = x2

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -1x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0, 1}