y^6-16y^2=0

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Solution for y^6-16y^2=0 equation: 


Simplifying
y6 + -16y2 = 0

Reorder the terms:
-16y2 + y6 = 0

Solving
-16y2 + y6 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y2'.
y2(-16 + y4) = 0

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

Factor a difference between two squares.
y2((4 + y2)((2 + y)(-2 + 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 '(4 + y2)' equal to zero and attempt to solve:

Simplifying
4 + y2 = 0

Solving
4 + y2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + y2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + y2 = 0 + -4
y2 = 0 + -4

Combine like terms: 0 + -4 = -4
y2 = -4

Simplifying
y2 = -4

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

Simplifying
2 + y = 0

Solving
2 + y = 0

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

Add '-2' to each side of the equation.
2 + -2 + y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + y = 0 + -2
y = 0 + -2

Combine like terms: 0 + -2 = -2
y = -2

Simplifying
y = -2

Subproblem 4
Set the factor '(-2 + y)' equal to zero and attempt to solve:

Simplifying
-2 + y = 0

Solving
-2 + y = 0

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

Add '2' to each side of the equation.
-2 + 2 + y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + y = 0 + 2
y = 0 + 2

Combine like terms: 0 + 2 = 2
y = 2

Simplifying
y = 2
Solution
y = {0, -2, 2}

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