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Simplifying 80h3 + -125hk2 = 0 Reorder the terms: -125hk2 + 80h3 = 0 Solving -125hk2 + 80h3 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '5h'. 5h(-25k2 + 16h2) = 0 Factor a difference between two squares. 5h((5k + 4h)(-5k + 4h)) = 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 '(5k + 4h)' equal to zero and attempt to solve: Simplifying 5k + 4h = 0 Reorder the terms: 4h + 5k = 0 Solving 4h + 5k = 0 Move all terms containing h to the left, all other terms to the right. Add '-5k' to each side of the equation. 4h + 5k + -5k = 0 + -5k Combine like terms: 5k + -5k = 0 4h + 0 = 0 + -5k 4h = 0 + -5k Remove the zero: 4h = -5k Divide each side by '4'. h = -1.25k Simplifying h = -1.25kSubproblem 3
Set the factor '(-5k + 4h)' equal to zero and attempt to solve: Simplifying -5k + 4h = 0 Reorder the terms: 4h + -5k = 0 Solving 4h + -5k = 0 Move all terms containing h to the left, all other terms to the right. Add '5k' to each side of the equation. 4h + -5k + 5k = 0 + 5k Combine like terms: -5k + 5k = 0 4h + 0 = 0 + 5k 4h = 0 + 5k Remove the zero: 4h = 5k Divide each side by '4'. h = 1.25k Simplifying h = 1.25kSolution
h = {0, -1.25k, 1.25k}
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