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Simplifying (h + -3)(4 + h) = 60 Reorder the terms: (-3 + h)(4 + h) = 60 Multiply (-3 + h) * (4 + h) (-3(4 + h) + h(4 + h)) = 60 ((4 * -3 + h * -3) + h(4 + h)) = 60 ((-12 + -3h) + h(4 + h)) = 60 (-12 + -3h + (4 * h + h * h)) = 60 (-12 + -3h + (4h + h2)) = 60 Combine like terms: -3h + 4h = 1h (-12 + 1h + h2) = 60 Solving -12 + 1h + h2 = 60 Solving for variable 'h'. Reorder the terms: -12 + -60 + 1h + h2 = 60 + -60 Combine like terms: -12 + -60 = -72 -72 + 1h + h2 = 60 + -60 Combine like terms: 60 + -60 = 0 -72 + 1h + h2 = 0 Factor a trinomial. (-9 + -1h)(8 + -1h) = 0Subproblem 1
Set the factor '(-9 + -1h)' equal to zero and attempt to solve: Simplifying -9 + -1h = 0 Solving -9 + -1h = 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 + -1h = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1h = 0 + 9 -1h = 0 + 9 Combine like terms: 0 + 9 = 9 -1h = 9 Divide each side by '-1'. h = -9 Simplifying h = -9Subproblem 2
Set the factor '(8 + -1h)' equal to zero and attempt to solve: Simplifying 8 + -1h = 0 Solving 8 + -1h = 0 Move all terms containing h to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1h = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1h = 0 + -8 -1h = 0 + -8 Combine like terms: 0 + -8 = -8 -1h = -8 Divide each side by '-1'. h = 8 Simplifying h = 8Solution
h = {-9, 8}
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