32z^5-2z=0

Solution for 32z^5-2z=0 equation:

Simplifying
32z5 + -2z = 0

Reorder the terms:
-2z + 32z5 = 0

Solving
-2z + 32z5 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2z'.
2z(-1 + 16z4) = 0

Factor a difference between two squares.
2z((1 + 4z2)(-1 + 4z2)) = 0

Factor a difference between two squares.
2z((1 + 4z2)((1 + 2z)(-1 + 2z))) = 0

Ignore the factor 2.
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 '(1 + 4z2)' equal to zero and attempt to solve:

Simplifying
1 + 4z2 = 0

Solving
1 + 4z2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4z2 = 0 + -1
4z2 = 0 + -1

Combine like terms: 0 + -1 = -1
4z2 = -1

Divide each side by '4'.
z2 = -0.25

Simplifying
z2 = -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 + 2z)' equal to zero and attempt to solve:

Simplifying
1 + 2z = 0

Solving
1 + 2z = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2z = 0 + -1

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

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

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

Simplifying
z = -0.5
Subproblem 4
Set the factor '(-1 + 2z)' equal to zero and attempt to solve:

Simplifying
-1 + 2z = 0

Solving
-1 + 2z = 0

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

Add '1' to each side of the equation.
-1 + 1 + 2z = 0 + 1

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

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

Divide each side by '2'.
z = 0.5

Simplifying
z = 0.5
Solution
z = {0, -0.5, 0.5}