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Simplifying (4h + 4)(2h + 5) = 0 Reorder the terms: (4 + 4h)(2h + 5) = 0 Reorder the terms: (4 + 4h)(5 + 2h) = 0 Multiply (4 + 4h) * (5 + 2h) (4(5 + 2h) + 4h * (5 + 2h)) = 0 ((5 * 4 + 2h * 4) + 4h * (5 + 2h)) = 0 ((20 + 8h) + 4h * (5 + 2h)) = 0 (20 + 8h + (5 * 4h + 2h * 4h)) = 0 (20 + 8h + (20h + 8h2)) = 0 Combine like terms: 8h + 20h = 28h (20 + 28h + 8h2) = 0 Solving 20 + 28h + 8h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + 7h + 2h2) = 0 Factor a trinomial. 4((5 + 2h)(1 + h)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + 2h)' equal to zero and attempt to solve: Simplifying 5 + 2h = 0 Solving 5 + 2h = 0 Move all terms containing h to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2h = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2h = 0 + -5 2h = 0 + -5 Combine like terms: 0 + -5 = -5 2h = -5 Divide each side by '2'. h = -2.5 Simplifying h = -2.5Subproblem 2
Set the factor '(1 + h)' equal to zero and attempt to solve: Simplifying 1 + h = 0 Solving 1 + h = 0 Move all terms containing h to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + h = 0 + -1 Combine like terms: 1 + -1 = 0 0 + h = 0 + -1 h = 0 + -1 Combine like terms: 0 + -1 = -1 h = -1 Simplifying h = -1Solution
h = {-2.5, -1}
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