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Simplifying -80h3 + 200h2y + -125hy2 = 0 Reorder the terms: -125hy2 + 200h2y + -80h3 = 0 Solving -125hy2 + 200h2y + -80h3 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '5h'. 5h(-25y2 + 40hy + -16h2) = 0 Factor a trinomial. 5h((-5y + 4h)(5y + -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 '(-5y + 4h)' equal to zero and attempt to solve: Simplifying -5y + 4h = 0 Reorder the terms: 4h + -5y = 0 Solving 4h + -5y = 0 Move all terms containing h to the left, all other terms to the right. Add '5y' to each side of the equation. 4h + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 4h + 0 = 0 + 5y 4h = 0 + 5y Remove the zero: 4h = 5y Divide each side by '4'. h = 1.25y Simplifying h = 1.25ySubproblem 3
Set the factor '(5y + -4h)' equal to zero and attempt to solve: Simplifying 5y + -4h = 0 Reorder the terms: -4h + 5y = 0 Solving -4h + 5y = 0 Move all terms containing h to the left, all other terms to the right. Add '-5y' to each side of the equation. -4h + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 -4h + 0 = 0 + -5y -4h = 0 + -5y Remove the zero: -4h = -5y Divide each side by '-4'. h = 1.25y Simplifying h = 1.25ySolution
h = {0, 1.25y, 1.25y}
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