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Simplifying (-4h + 2)(3h + 7) = 0 Reorder the terms: (2 + -4h)(3h + 7) = 0 Reorder the terms: (2 + -4h)(7 + 3h) = 0 Multiply (2 + -4h) * (7 + 3h) (2(7 + 3h) + -4h * (7 + 3h)) = 0 ((7 * 2 + 3h * 2) + -4h * (7 + 3h)) = 0 ((14 + 6h) + -4h * (7 + 3h)) = 0 (14 + 6h + (7 * -4h + 3h * -4h)) = 0 (14 + 6h + (-28h + -12h2)) = 0 Combine like terms: 6h + -28h = -22h (14 + -22h + -12h2) = 0 Solving 14 + -22h + -12h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -11h + -6h2) = 0 Factor a trinomial. 2((1 + -2h)(7 + 3h)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -2h)' equal to zero and attempt to solve: Simplifying 1 + -2h = 0 Solving 1 + -2h = 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 + -2h = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2h = 0 + -1 -2h = 0 + -1 Combine like terms: 0 + -1 = -1 -2h = -1 Divide each side by '-2'. h = 0.5 Simplifying h = 0.5Subproblem 2
Set the factor '(7 + 3h)' equal to zero and attempt to solve: Simplifying 7 + 3h = 0 Solving 7 + 3h = 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 + 3h = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3h = 0 + -7 3h = 0 + -7 Combine like terms: 0 + -7 = -7 3h = -7 Divide each side by '3'. h = -2.333333333 Simplifying h = -2.333333333Solution
h = {0.5, -2.333333333}
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