0=-h^3+36h

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Solution for 0=-h^3+36h equation:


Simplifying
0 = -1h3 + 36h

Reorder the terms:
0 = 36h + -1h3

Solving
0 = 36h + -1h3

Solving for variable 'h'.
Remove the zero:
-36h + h3 = 36h + -1h3 + -36h + h3

Reorder the terms:
-36h + h3 = 36h + -36h + -1h3 + h3

Combine like terms: 36h + -36h = 0
-36h + h3 = 0 + -1h3 + h3
-36h + h3 = -1h3 + h3

Combine like terms: -1h3 + h3 = 0
-36h + h3 = 0

Factor out the Greatest Common Factor (GCF), 'h'.
h(-36 + h2) = 0

Factor a difference between two squares.
h((6 + h)(-6 + 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 '(6 + h)' equal to zero and attempt to solve: Simplifying 6 + h = 0 Solving 6 + h = 0 Move all terms containing h to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + h = 0 + -6 Combine like terms: 6 + -6 = 0 0 + h = 0 + -6 h = 0 + -6 Combine like terms: 0 + -6 = -6 h = -6 Simplifying h = -6

Subproblem 3

Set the factor '(-6 + h)' equal to zero and attempt to solve: Simplifying -6 + h = 0 Solving -6 + h = 0 Move all terms containing h to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + h = 0 + 6 Combine like terms: -6 + 6 = 0 0 + h = 0 + 6 h = 0 + 6 Combine like terms: 0 + 6 = 6 h = 6 Simplifying h = 6

Solution

h = {0, -6, 6}

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