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Simplifying (2h + 4)(3h + 2) = 0 Reorder the terms: (4 + 2h)(3h + 2) = 0 Reorder the terms: (4 + 2h)(2 + 3h) = 0 Multiply (4 + 2h) * (2 + 3h) (4(2 + 3h) + 2h * (2 + 3h)) = 0 ((2 * 4 + 3h * 4) + 2h * (2 + 3h)) = 0 ((8 + 12h) + 2h * (2 + 3h)) = 0 (8 + 12h + (2 * 2h + 3h * 2h)) = 0 (8 + 12h + (4h + 6h2)) = 0 Combine like terms: 12h + 4h = 16h (8 + 16h + 6h2) = 0 Solving 8 + 16h + 6h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 8h + 3h2) = 0 Factor a trinomial. 2((2 + h)(2 + 3h)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + h)' equal to zero and attempt to solve: Simplifying 2 + h = 0 Solving 2 + h = 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 + h = 0 + -2 Combine like terms: 2 + -2 = 0 0 + h = 0 + -2 h = 0 + -2 Combine like terms: 0 + -2 = -2 h = -2 Simplifying h = -2Subproblem 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 = -0.6666666667Solution
h = {-2, -0.6666666667}
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