z^5-256z=0

Solution for z^5-256z=0 equation:

Simplifying
z5 + -256z = 0

Reorder the terms:
-256z + z5 = 0

Solving
-256z + z5 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-256 + z4) = 0

Factor a difference between two squares.
z((16 + z2)(-16 + z2)) = 0

Factor a difference between two squares.
z((16 + z2)((4 + z)(-4 + z))) = 0

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

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(16 + z2)' equal to zero and attempt to solve:

Simplifying
16 + z2 = 0

Solving
16 + z2 = 0

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

Add '-16' to each side of the equation.
16 + -16 + z2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + z2 = 0 + -16
z2 = 0 + -16

Combine like terms: 0 + -16 = -16
z2 = -16

Simplifying
z2 = -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 + z)' equal to zero and attempt to solve:

Simplifying
4 + z = 0

Solving
4 + z = 0

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

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

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

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

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

Simplifying
-4 + z = 0

Solving
-4 + z = 0

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

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

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

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

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