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Simplifying -20h3 + 60h2y + -45hy2 = 0 Reorder the terms: -45hy2 + 60h2y + -20h3 = 0 Solving -45hy2 + 60h2y + -20h3 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '5h'. 5h(-9y2 + 12hy + -4h2) = 0 Factor a trinomial. 5h((-3y + 2h)(3y + -2h)) = 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 '(-3y + 2h)' equal to zero and attempt to solve: Simplifying -3y + 2h = 0 Reorder the terms: 2h + -3y = 0 Solving 2h + -3y = 0 Move all terms containing h to the left, all other terms to the right. Add '3y' to each side of the equation. 2h + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 2h + 0 = 0 + 3y 2h = 0 + 3y Remove the zero: 2h = 3y Divide each side by '2'. h = 1.5y Simplifying h = 1.5ySubproblem 3
Set the factor '(3y + -2h)' equal to zero and attempt to solve: Simplifying 3y + -2h = 0 Reorder the terms: -2h + 3y = 0 Solving -2h + 3y = 0 Move all terms containing h to the left, all other terms to the right. Add '-3y' to each side of the equation. -2h + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 -2h + 0 = 0 + -3y -2h = 0 + -3y Remove the zero: -2h = -3y Divide each side by '-2'. h = 1.5y Simplifying h = 1.5ySolution
h = {0, 1.5y, 1.5y}
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