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Simplifying -75h3 + 60h2y + -12hy2 = 0 Reorder the terms: -12hy2 + 60h2y + -75h3 = 0 Solving -12hy2 + 60h2y + -75h3 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '3h'. 3h(-4y2 + 20hy + -25h2) = 0 Factor a trinomial. 3h((-2y + 5h)(2y + -5h)) = 0 Ignore the factor 3.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 '(-2y + 5h)' equal to zero and attempt to solve: Simplifying -2y + 5h = 0 Reorder the terms: 5h + -2y = 0 Solving 5h + -2y = 0 Move all terms containing h to the left, all other terms to the right. Add '2y' to each side of the equation. 5h + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 5h + 0 = 0 + 2y 5h = 0 + 2y Remove the zero: 5h = 2y Divide each side by '5'. h = 0.4y Simplifying h = 0.4ySubproblem 3
Set the factor '(2y + -5h)' equal to zero and attempt to solve: Simplifying 2y + -5h = 0 Reorder the terms: -5h + 2y = 0 Solving -5h + 2y = 0 Move all terms containing h to the left, all other terms to the right. Add '-2y' to each side of the equation. -5h + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 -5h + 0 = 0 + -2y -5h = 0 + -2y Remove the zero: -5h = -2y Divide each side by '-5'. h = 0.4y Simplifying h = 0.4ySolution
h = {0, 0.4y, 0.4y}
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