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Simplifying 9h(h + -4)(3h + 2) = 0 Reorder the terms: 9h(-4 + h)(3h + 2) = 0 Reorder the terms: 9h(-4 + h)(2 + 3h) = 0 Multiply (-4 + h) * (2 + 3h) 9h(-4(2 + 3h) + h(2 + 3h)) = 0 9h((2 * -4 + 3h * -4) + h(2 + 3h)) = 0 9h((-8 + -12h) + h(2 + 3h)) = 0 9h(-8 + -12h + (2 * h + 3h * h)) = 0 9h(-8 + -12h + (2h + 3h2)) = 0 Combine like terms: -12h + 2h = -10h 9h(-8 + -10h + 3h2) = 0 (-8 * 9h + -10h * 9h + 3h2 * 9h) = 0 (-72h + -90h2 + 27h3) = 0 Solving -72h + -90h2 + 27h3 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '9h'. 9h(-8 + -10h + 3h2) = 0 Factor a trinomial. 9h((-2 + -3h)(4 + -1h)) = 0 Ignore the factor 9.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 '(-2 + -3h)' equal to zero and attempt to solve: Simplifying -2 + -3h = 0 Solving -2 + -3h = 0 Move all terms containing h to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3h = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3h = 0 + 2 -3h = 0 + 2 Combine like terms: 0 + 2 = 2 -3h = 2 Divide each side by '-3'. h = -0.6666666667 Simplifying h = -0.6666666667Subproblem 3
Set the factor '(4 + -1h)' equal to zero and attempt to solve: Simplifying 4 + -1h = 0 Solving 4 + -1h = 0 Move all terms containing h to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1h = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1h = 0 + -4 -1h = 0 + -4 Combine like terms: 0 + -4 = -4 -1h = -4 Divide each side by '-1'. h = 4 Simplifying h = 4Solution
h = {0, -0.6666666667, 4}
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