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Simplifying -75h3 + 90h2y + -27hy2 = 0 Reorder the terms: -27hy2 + 90h2y + -75h3 = 0 Solving -27hy2 + 90h2y + -75h3 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '3h'. 3h(-9y2 + 30hy + -25h2) = 0 Factor a trinomial. 3h((-3y + 5h)(3y + -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 '(-3y + 5h)' equal to zero and attempt to solve: Simplifying -3y + 5h = 0 Reorder the terms: 5h + -3y = 0 Solving 5h + -3y = 0 Move all terms containing h to the left, all other terms to the right. Add '3y' to each side of the equation. 5h + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 5h + 0 = 0 + 3y 5h = 0 + 3y Remove the zero: 5h = 3y Divide each side by '5'. h = 0.6y Simplifying h = 0.6ySubproblem 3
Set the factor '(3y + -5h)' equal to zero and attempt to solve: Simplifying 3y + -5h = 0 Reorder the terms: -5h + 3y = 0 Solving -5h + 3y = 0 Move all terms containing h to the left, all other terms to the right. Add '-3y' to each side of the equation. -5h + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 -5h + 0 = 0 + -3y -5h = 0 + -3y Remove the zero: -5h = -3y Divide each side by '-5'. h = 0.6y Simplifying h = 0.6ySolution
h = {0, 0.6y, 0.6y}
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