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Simplifying -3h(2h + -5y)(2h + -5y) = 0 Multiply (2h + -5y) * (2h + -5y) -3h(2h * (2h + -5y) + -5y * (2h + -5y)) = 0 -3h((2h * 2h + -5y * 2h) + -5y * (2h + -5y)) = 0 Reorder the terms: -3h((-10hy + 4h2) + -5y * (2h + -5y)) = 0 -3h((-10hy + 4h2) + -5y * (2h + -5y)) = 0 -3h(-10hy + 4h2 + (2h * -5y + -5y * -5y)) = 0 -3h(-10hy + 4h2 + (-10hy + 25y2)) = 0 Reorder the terms: -3h(-10hy + -10hy + 4h2 + 25y2) = 0 Combine like terms: -10hy + -10hy = -20hy -3h(-20hy + 4h2 + 25y2) = 0 (-20hy * -3h + 4h2 * -3h + 25y2 * -3h) = 0 Reorder the terms: (-75hy2 + 60h2y + -12h3) = 0 (-75hy2 + 60h2y + -12h3) = 0 Solving -75hy2 + 60h2y + -12h3 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '3h'. 3h(-25y2 + 20hy + -4h2) = 0 Factor a trinomial. 3h((-5y + 2h)(5y + -2h)) = 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 '(-5y + 2h)' equal to zero and attempt to solve: Simplifying -5y + 2h = 0 Reorder the terms: 2h + -5y = 0 Solving 2h + -5y = 0 Move all terms containing h to the left, all other terms to the right. Add '5y' to each side of the equation. 2h + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 2h + 0 = 0 + 5y 2h = 0 + 5y Remove the zero: 2h = 5y Divide each side by '2'. h = 2.5y Simplifying h = 2.5ySubproblem 3
Set the factor '(5y + -2h)' equal to zero and attempt to solve: Simplifying 5y + -2h = 0 Reorder the terms: -2h + 5y = 0 Solving -2h + 5y = 0 Move all terms containing h to the left, all other terms to the right. Add '-5y' to each side of the equation. -2h + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 -2h + 0 = 0 + -5y -2h = 0 + -5y Remove the zero: -2h = -5y Divide each side by '-2'. h = 2.5y Simplifying h = 2.5ySolution
h = {0, 2.5y, 2.5y}
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