64h^5+24h^3-4h=0

Solution for 64h^5+24h^3-4h=0 equation:

Simplifying
64h5 + 24h3 + -4h = 0

Reorder the terms:
-4h + 24h3 + 64h5 = 0

Solving
-4h + 24h3 + 64h5 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '4h'.
4h(-1 + 6h2 + 16h4) = 0

Factor a trinomial.
4h((-1 + -2h2)(1 + -8h2)) = 0

Ignore the factor 4.
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 + -2h2)' equal to zero and attempt to solve:

Simplifying
-1 + -2h2 = 0

Solving
-1 + -2h2 = 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 + -2h2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2h2 = 0 + 1
-2h2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2h2 = 1

Divide each side by '-2'.
h2 = -0.5

Simplifying
h2 = -0.5

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 + -8h2)' equal to zero and attempt to solve:

Simplifying
1 + -8h2 = 0

Solving
1 + -8h2 = 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 + -8h2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8h2 = 0 + -1
-8h2 = 0 + -1

Combine like terms: 0 + -1 = -1
-8h2 = -1

Divide each side by '-8'.
h2 = 0.125

Simplifying
h2 = 0.125

Take the square root of each side:
h = {-0.353553391, 0.353553391}
Solution
h = {0, -0.353553391, 0.353553391}