-32h^3+80h^2y-50hy^2=0

Solution for -32h^3+80h^2y-50hy^2=0 equation:

Simplifying
-32h3 + 80h2y + -50hy2 = 0

Reorder the terms:
-50hy2 + 80h2y + -32h3 = 0

Solving
-50hy2 + 80h2y + -32h3 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '2h'.
2h(-25y2 + 40hy + -16h2) = 0

Factor a trinomial.
2h((-5y + 4h)(5y + -4h)) = 0

Ignore the factor 2.
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 '(-5y + 4h)' equal to zero and attempt to solve:

Simplifying
-5y + 4h = 0

Reorder the terms:
4h + -5y = 0

Solving
4h + -5y = 0

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

Add '5y' to each side of the equation.
4h + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
4h + 0 = 0 + 5y
4h = 0 + 5y
Remove the zero:
4h = 5y

Divide each side by '4'.
h = 1.25y

Simplifying
h = 1.25y
Subproblem 3
Set the factor '(5y + -4h)' equal to zero and attempt to solve:

Simplifying
5y + -4h = 0

Reorder the terms:
-4h + 5y = 0

Solving
-4h + 5y = 0

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

Add '-5y' to each side of the equation.
-4h + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
-4h + 0 = 0 + -5y
-4h = 0 + -5y
Remove the zero:
-4h = -5y

Divide each side by '-4'.
h = 1.25y

Simplifying
h = 1.25y
Solution
h = {0, 1.25y, 1.25y}