5y(4y^4+1)(4y^4-1)=

Solution for 5y(4y^4+1)(4y^4-1)= equation:

Simplifying
5y(4y4 + 1)(4y4 + -1) = 0

Reorder the terms:
5y(1 + 4y4)(4y4 + -1) = 0

Reorder the terms:
5y(1 + 4y4)(-1 + 4y4) = 0

Multiply (1 + 4y4) * (-1 + 4y4)
5y(1(-1 + 4y4) + 4y4 * (-1 + 4y4)) = 0
5y((-1 * 1 + 4y4 * 1) + 4y4 * (-1 + 4y4)) = 0
5y((-1 + 4y4) + 4y4 * (-1 + 4y4)) = 0
5y(-1 + 4y4 + (-1 * 4y4 + 4y4 * 4y4)) = 0
5y(-1 + 4y4 + (-4y4 + 16y8)) = 0

Combine like terms: 4y4 + -4y4 = 0
5y(-1 + 0 + 16y8) = 0
5y(-1 + 16y8) = 0
(-1 * 5y + 16y8 * 5y) = 0
(-5y + 80y9) = 0

Solving
-5y + 80y9 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y'.
5y(-1 + 16y8) = 0

Factor a difference between two squares.
5y((1 + 4y4)(-1 + 4y4)) = 0

Factor a difference between two squares.
5y((1 + 4y4)((1 + 2y2)(-1 + 2y2))) = 0

Ignore the factor 5.
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 + 4y4)' equal to zero and attempt to solve:

Simplifying
1 + 4y4 = 0

Solving
1 + 4y4 = 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 + 4y4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4y4 = 0 + -1
4y4 = 0 + -1

Combine like terms: 0 + -1 = -1
4y4 = -1

Divide each side by '4'.
y4 = -0.25

Simplifying
y4 = -0.25

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 + 2y2)' equal to zero and attempt to solve:

Simplifying
1 + 2y2 = 0

Solving
1 + 2y2 = 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 + 2y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2y2 = 0 + -1
2y2 = 0 + -1

Combine like terms: 0 + -1 = -1
2y2 = -1

Divide each side by '2'.
y2 = -0.5

Simplifying
y2 = -0.5

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 + 2y2)' equal to zero and attempt to solve:

Simplifying
-1 + 2y2 = 0

Solving
-1 + 2y2 = 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 + 2y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2y2 = 0 + 1
2y2 = 0 + 1

Combine like terms: 0 + 1 = 1
2y2 = 1

Divide each side by '2'.
y2 = 0.5

Simplifying
y2 = 0.5

Take the square root of each side:
y = {-0.707106781, 0.707106781}
Solution
y = {0, -0.707106781, 0.707106781}