(X^2-1)y=0

Solution for (X^2-1)y=0 equation:

Simplifying
(X2 + -1) * y = 0

Reorder the terms:
(-1 + X2) * y = 0

Reorder the terms for easier multiplication:
y(-1 + X2) = 0
(-1 * y + X2 * y) = 0
(-1y + yX2) = 0

Solving
-1y + yX2 = 0

Solving for variable 'y'.

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

Factor out the Greatest Common Factor (GCF), 'y'.
y(-1 + X2) = 0

Factor a difference between two squares.
y((1 + X)(-1 + X)) = 0

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

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 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 y 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.
Subproblem 3
Set the factor '(-1 + X)' equal to zero and attempt to solve:

Simplifying
-1 + X = 0

Solving
-1 + X = 0

Move all terms containing y 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
y = {0}