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

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

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

Reorder the terms:
0 = (-1 + x2) + -1(x + -1)

Remove parenthesis around (-1 + x2)
0 = -1 + x2 + -1(x + -1)

Reorder the terms:
0 = -1 + x2 + -1(-1 + x)
0 = -1 + x2 + (-1 * -1 + x * -1)
0 = -1 + x2 + (1 + -1x)

Reorder the terms:
0 = -1 + 1 + -1x + x2

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

Solving
0 = -1x + x2

Solving for variable 'x'.
Remove the zero:
x + -1x2 = -1x + x2 + x + -1x2

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

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

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}