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Simplifying (3 + 2h) * h = 27 Reorder the terms for easier multiplication: h(3 + 2h) = 27 (3 * h + 2h * h) = 27 (3h + 2h2) = 27 Solving 3h + 2h2 = 27 Solving for variable 'h'. Reorder the terms: -27 + 3h + 2h2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 3h + 2h2 = 0 Factor a trinomial. (-9 + -2h)(3 + -1h) = 0Subproblem 1
Set the factor '(-9 + -2h)' equal to zero and attempt to solve: Simplifying -9 + -2h = 0 Solving -9 + -2h = 0 Move all terms containing h to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2h = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2h = 0 + 9 -2h = 0 + 9 Combine like terms: 0 + 9 = 9 -2h = 9 Divide each side by '-2'. h = -4.5 Simplifying h = -4.5Subproblem 2
Set the factor '(3 + -1h)' equal to zero and attempt to solve: Simplifying 3 + -1h = 0 Solving 3 + -1h = 0 Move all terms containing h to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1h = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1h = 0 + -3 -1h = 0 + -3 Combine like terms: 0 + -3 = -3 -1h = -3 Divide each side by '-1'. h = 3 Simplifying h = 3Solution
h = {-4.5, 3}
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