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Simplifying 2h3 + 15h = 31h2 Reorder the terms: 15h + 2h3 = 31h2 Solving 15h + 2h3 = 31h2 Solving for variable 'h'. Reorder the terms: 15h + -31h2 + 2h3 = 31h2 + -31h2 Combine like terms: 31h2 + -31h2 = 0 15h + -31h2 + 2h3 = 0 Factor out the Greatest Common Factor (GCF), 'h'. h(15 + -31h + 2h2) = 0 Factor a trinomial. h((1 + -2h)(15 + -1h)) = 0Subproblem 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 '(1 + -2h)' equal to zero and attempt to solve: Simplifying 1 + -2h = 0 Solving 1 + -2h = 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 + -2h = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2h = 0 + -1 -2h = 0 + -1 Combine like terms: 0 + -1 = -1 -2h = -1 Divide each side by '-2'. h = 0.5 Simplifying h = 0.5Subproblem 3
Set the factor '(15 + -1h)' equal to zero and attempt to solve: Simplifying 15 + -1h = 0 Solving 15 + -1h = 0 Move all terms containing h to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1h = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1h = 0 + -15 -1h = 0 + -15 Combine like terms: 0 + -15 = -15 -1h = -15 Divide each side by '-1'. h = 15 Simplifying h = 15Solution
h = {0, 0.5, 15}
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