4y(1-y^8)=0

Solution for 4y(1-y^8)=0 equation:

Simplifying
4y(1 + -1y8) = 0
(1 * 4y + -1y8 * 4y) = 0
(4y + -4y9) = 0

Solving
4y + -4y9 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4y'.
4y(1 + -1y8) = 0

Factor a difference between two squares.
4y((1 + y4)(1 + -1y4)) = 0

Factor a difference between two squares.
4y((1 + y4)((1 + y2)(1 + -1y2))) = 0

Factor a difference between two squares.
4y((1 + y4)((1 + y2)((1 + y)(1 + -1y)))) = 0

Ignore the factor 4.
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 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

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

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

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

Divide each side by '-1'.
y = 1

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