z^5-4z=0

Solution for z^5-4z=0 equation:

Simplifying
z5 + -4z = 0

Reorder the terms:
-4z + z5 = 0

Solving
-4z + z5 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-4 + z4) = 0

Factor a difference between two squares.
z((2 + z2)(-2 + z2)) = 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 '(2 + z2)' equal to zero and attempt to solve:

Simplifying
2 + z2 = 0

Solving
2 + z2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + z2 = 0 + -2
z2 = 0 + -2

Combine like terms: 0 + -2 = -2
z2 = -2

Simplifying
z2 = -2

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 + z2)' equal to zero and attempt to solve:

Simplifying
-2 + z2 = 0

Solving
-2 + z2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + z2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + z2 = 0 + 2
z2 = 0 + 2

Combine like terms: 0 + 2 = 2
z2 = 2

Simplifying
z2 = 2

Take the square root of each side:
z = {-1.414213562, 1.414213562}
Solution
z = {0, -1.414213562, 1.414213562}