y(y^8-1)=0

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Solution for y(y^8-1)=0 equation: 


Simplifying
y(y8 + -1) = 0

Reorder the terms:
y(-1 + y8) = 0
(-1 * y + y8 * y) = 0
(-1y + y9) = 0

Solving
-1y + y9 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-1 + y8) = 0

Factor a difference between two squares.
y((1 + y4)(-1 + y4)) = 0

Factor a difference between two squares.
y((1 + y4)((1 + y2)(-1 + y2))) = 0

Factor a difference between two squares.
y((1 + y4)((1 + y2)((1 + y)(-1 + y)))) = 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 + y4)' equal to zero and attempt to solve:

Simplifying
1 + y4 = 0

Solving
1 + y4 = 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 + y4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + y4 = 0 + -1
y4 = 0 + -1

Combine like terms: 0 + -1 = -1
y4 = -1

Simplifying
y4 = -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 + 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 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

Subproblem 5
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}

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