20h^3-5h=0

Solution for 20h^3-5h=0 equation:

Simplifying
20h3 + -5h = 0

Reorder the terms:
-5h + 20h3 = 0

Solving
-5h + 20h3 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '5h'.
5h(-1 + 4h2) = 0

Factor a difference between two squares.
5h((1 + 2h)(-1 + 2h)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'h' equal to zero and attempt to solve:

Simplifying
h = 0

Solving
h = 0

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

Simplifying
h = 0
Subproblem 2
Set the factor '(1 + 2h)' equal to zero and attempt to solve:

Simplifying
1 + 2h = 0

Solving
1 + 2h = 0

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

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

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

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

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

Simplifying
h = -0.5
Subproblem 3
Set the factor '(-1 + 2h)' equal to zero and attempt to solve:

Simplifying
-1 + 2h = 0

Solving
-1 + 2h = 0

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

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

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

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

Divide each side by '2'.
h = 0.5

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