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Simplifying -32h3 + 48h2y + -18hy2 = 0 Reorder the terms: -18hy2 + 48h2y + -32h3 = 0 Solving -18hy2 + 48h2y + -32h3 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '2h'. 2h(-9y2 + 24hy + -16h2) = 0 Factor a trinomial. 2h((-3y + 4h)(3y + -4h)) = 0 Ignore the factor 2.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 + 4h)' equal to zero and attempt to solve: Simplifying -3y + 4h = 0 Reorder the terms: 4h + -3y = 0 Solving 4h + -3y = 0 Move all terms containing h to the left, all other terms to the right. Add '3y' to each side of the equation. 4h + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 4h + 0 = 0 + 3y 4h = 0 + 3y Remove the zero: 4h = 3y Divide each side by '4'. h = 0.75y Simplifying h = 0.75ySubproblem 3
Set the factor '(3y + -4h)' equal to zero and attempt to solve: Simplifying 3y + -4h = 0 Reorder the terms: -4h + 3y = 0 Solving -4h + 3y = 0 Move all terms containing h to the left, all other terms to the right. Add '-3y' to each side of the equation. -4h + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 -4h + 0 = 0 + -3y -4h = 0 + -3y Remove the zero: -4h = -3y Divide each side by '-4'. h = 0.75y Simplifying h = 0.75ySolution
h = {0, 0.75y, 0.75y}
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