y^6-y^2=0

Solution for y^6-y^2=0 equation:

Simplifying
y6 + -1y2 = 0

Reorder the terms:
-1y2 + y6 = 0

Solving
-1y2 + y6 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y2'.
y2(-1 + y4) = 0

Factor a difference between two squares.
y2((1 + y2)(-1 + y2)) = 0

Factor a difference between two squares.
y2((1 + y2)((1 + y)(-1 + y))) = 0

Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

Take the square root of each side:
y = {0}
Subproblem 2
Set the factor '(1 + y2)' equal to zero and attempt to solve:

Simplifying
1 + y2 = 0

Solving
1 + y2 = 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 + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + y2 = 0 + -1
y2 = 0 + -1

Combine like terms: 0 + -1 = -1
y2 = -1

Simplifying
y2 = -1

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 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 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 + y = 0 + -1

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

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

Simplifying
y = -1
Subproblem 4
Set the factor '(-1 + y)' equal to zero and attempt to solve:

Simplifying
-1 + y = 0

Solving
-1 + y = 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 + y = 0 + 1

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

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

Simplifying
y = 1
Solution
y = {0, -1, 1}