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Simplifying 840 = (12)(3 + h)(h) Reorder the terms for easier multiplication: 840 = 12h(3 + h) 840 = (3 * 12h + h * 12h) 840 = (36h + 12h2) Solving 840 = 36h + 12h2 Solving for variable 'h'. Reorder the terms: 840 + -36h + -12h2 = 36h + -36h + 12h2 + -12h2 Combine like terms: 36h + -36h = 0 840 + -36h + -12h2 = 0 + 12h2 + -12h2 840 + -36h + -12h2 = 12h2 + -12h2 Combine like terms: 12h2 + -12h2 = 0 840 + -36h + -12h2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(70 + -3h + -1h2) = 0 Factor a trinomial. 12((7 + -1h)(10 + h)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(7 + -1h)' equal to zero and attempt to solve: Simplifying 7 + -1h = 0 Solving 7 + -1h = 0 Move all terms containing h to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1h = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1h = 0 + -7 -1h = 0 + -7 Combine like terms: 0 + -7 = -7 -1h = -7 Divide each side by '-1'. h = 7 Simplifying h = 7Subproblem 2
Set the factor '(10 + h)' equal to zero and attempt to solve: Simplifying 10 + h = 0 Solving 10 + h = 0 Move all terms containing h to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + h = 0 + -10 Combine like terms: 10 + -10 = 0 0 + h = 0 + -10 h = 0 + -10 Combine like terms: 0 + -10 = -10 h = -10 Simplifying h = -10Solution
h = {7, -10}
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