6h=4h^3+5h^2

Solution for 6h=4h^3+5h^2 equation:

Simplifying
6h = 4h3 + 5h2

Reorder the terms:
6h = 5h2 + 4h3

Solving
6h = 5h2 + 4h3

Solving for variable 'h'.

Reorder the terms:
6h + -5h2 + -4h3 = 5h2 + -5h2 + 4h3 + -4h3

Combine like terms: 5h2 + -5h2 = 0
6h + -5h2 + -4h3 = 0 + 4h3 + -4h3
6h + -5h2 + -4h3 = 4h3 + -4h3

Combine like terms: 4h3 + -4h3 = 0
6h + -5h2 + -4h3 = 0

Factor out the Greatest Common Factor (GCF), 'h'.
h(6 + -5h + -4h2) = 0

Factor a trinomial.
h((3 + -4h)(2 + h)) = 0

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 '(3 + -4h)' equal to zero and attempt to solve:

Simplifying
3 + -4h = 0

Solving
3 + -4h = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4h = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4h = 0 + -3
-4h = 0 + -3

Combine like terms: 0 + -3 = -3
-4h = -3

Divide each side by '-4'.
h = 0.75

Simplifying
h = 0.75
Subproblem 3
Set the factor '(2 + h)' equal to zero and attempt to solve:

Simplifying
2 + h = 0

Solving
2 + h = 0

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

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

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

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

Simplifying
h = -2
Solution
h = {0, 0.75, -2}