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Simplifying -100h3 + 160h2y + -64hy2 = 0 Reorder the terms: -64hy2 + 160h2y + -100h3 = 0 Solving -64hy2 + 160h2y + -100h3 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '4h'. 4h(-16y2 + 40hy + -25h2) = 0 Factor a trinomial. 4h((-4y + 5h)(4y + -5h)) = 0 Ignore the factor 4.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 '(-4y + 5h)' equal to zero and attempt to solve: Simplifying -4y + 5h = 0 Reorder the terms: 5h + -4y = 0 Solving 5h + -4y = 0 Move all terms containing h to the left, all other terms to the right. Add '4y' to each side of the equation. 5h + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 5h + 0 = 0 + 4y 5h = 0 + 4y Remove the zero: 5h = 4y Divide each side by '5'. h = 0.8y Simplifying h = 0.8ySubproblem 3
Set the factor '(4y + -5h)' equal to zero and attempt to solve: Simplifying 4y + -5h = 0 Reorder the terms: -5h + 4y = 0 Solving -5h + 4y = 0 Move all terms containing h to the left, all other terms to the right. Add '-4y' to each side of the equation. -5h + 4y + -4y = 0 + -4y Combine like terms: 4y + -4y = 0 -5h + 0 = 0 + -4y -5h = 0 + -4y Remove the zero: -5h = -4y Divide each side by '-5'. h = 0.8y Simplifying h = 0.8ySolution
h = {0, 0.8y, 0.8y}
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