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Simplifying -45h3 + 120h2 + -80h = 0 Reorder the terms: -80h + 120h2 + -45h3 = 0 Solving -80h + 120h2 + -45h3 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '5h'. 5h(-16 + 24h + -9h2) = 0 Factor a trinomial. 5h((-4 + 3h)(4 + -3h)) = 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 = 0Subproblem 2
Set the factor '(-4 + 3h)' equal to zero and attempt to solve: Simplifying -4 + 3h = 0 Solving -4 + 3h = 0 Move all terms containing h to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 3h = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3h = 0 + 4 3h = 0 + 4 Combine like terms: 0 + 4 = 4 3h = 4 Divide each side by '3'. h = 1.333333333 Simplifying h = 1.333333333Subproblem 3
Set the factor '(4 + -3h)' equal to zero and attempt to solve: Simplifying 4 + -3h = 0 Solving 4 + -3h = 0 Move all terms containing h to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3h = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3h = 0 + -4 -3h = 0 + -4 Combine like terms: 0 + -4 = -4 -3h = -4 Divide each side by '-3'. h = 1.333333333 Simplifying h = 1.333333333Solution
h = {0, 1.333333333, 1.333333333}
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