x^6-256x^2=

Solution for x^6-256x^2= equation:

Simplifying
x6 + -256x2 = 0

Reorder the terms:
-256x2 + x6 = 0

Solving
-256x2 + x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-256 + x4) = 0

Factor a difference between two squares.
x2((16 + x2)(-16 + x2)) = 0

Factor a difference between two squares.
x2((16 + x2)((4 + x)(-4 + x))) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(16 + x2)' equal to zero and attempt to solve:

Simplifying
16 + x2 = 0

Solving
16 + x2 = 0

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

Add '-16' to each side of the equation.
16 + -16 + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x2 = 0 + -16
x2 = 0 + -16

Combine like terms: 0 + -16 = -16
x2 = -16

Simplifying
x2 = -16

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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

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

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

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

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

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

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

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4
Solution
x = {0, -4, 4}