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Simplifying 4h3 = -13h2 + 12h Reorder the terms: 4h3 = 12h + -13h2 Solving 4h3 = 12h + -13h2 Solving for variable 'h'. Reorder the terms: -12h + 13h2 + 4h3 = 12h + -13h2 + -12h + 13h2 Reorder the terms: -12h + 13h2 + 4h3 = 12h + -12h + -13h2 + 13h2 Combine like terms: 12h + -12h = 0 -12h + 13h2 + 4h3 = 0 + -13h2 + 13h2 -12h + 13h2 + 4h3 = -13h2 + 13h2 Combine like terms: -13h2 + 13h2 = 0 -12h + 13h2 + 4h3 = 0 Factor out the Greatest Common Factor (GCF), 'h'. h(-12 + 13h + 4h2) = 0 Factor a trinomial. h((-4 + -1h)(3 + -4h)) = 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 '(-4 + -1h)' equal to zero and attempt to solve: Simplifying -4 + -1h = 0 Solving -4 + -1h = 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 + -1h = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1h = 0 + 4 -1h = 0 + 4 Combine like terms: 0 + 4 = 4 -1h = 4 Divide each side by '-1'. h = -4 Simplifying h = -4Subproblem 3
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 = 0.75Solution
h = {0, -4, 0.75}
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