(X+1)(x-1)-(x-1)=0

Solution for (X+1)(x-1)-(x-1)=0 equation:

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

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

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

Multiply (1 + X) * (-1 + x)
(1(-1 + x) + X(-1 + x)) + -1(x + -1) = 0
((-1 * 1 + x * 1) + X(-1 + x)) + -1(x + -1) = 0
((-1 + 1x) + X(-1 + x)) + -1(x + -1) = 0
(-1 + 1x + (-1 * X + x * X)) + -1(x + -1) = 0
(-1 + 1x + (-1X + xX)) + -1(x + -1) = 0

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

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

Reorder the terms:
-1 + 1 + -1X + 1x + -1x + xX = 0

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

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

Solving
-1X + xX = 0

Solving for variable 'X'.

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

Factor out the Greatest Common Factor (GCF), 'X'.
X(-1 + x) = 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 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 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 + x = 0 + 1

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

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

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

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

Simplifying
0 = 1 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
X = {0}