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Simplifying (3h + -7)(3h + -6) = 0 Reorder the terms: (-7 + 3h)(3h + -6) = 0 Reorder the terms: (-7 + 3h)(-6 + 3h) = 0 Multiply (-7 + 3h) * (-6 + 3h) (-7(-6 + 3h) + 3h * (-6 + 3h)) = 0 ((-6 * -7 + 3h * -7) + 3h * (-6 + 3h)) = 0 ((42 + -21h) + 3h * (-6 + 3h)) = 0 (42 + -21h + (-6 * 3h + 3h * 3h)) = 0 (42 + -21h + (-18h + 9h2)) = 0 Combine like terms: -21h + -18h = -39h (42 + -39h + 9h2) = 0 Solving 42 + -39h + 9h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '3'. 3(14 + -13h + 3h2) = 0 Factor a trinomial. 3((2 + -1h)(7 + -3h)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -1h)' equal to zero and attempt to solve: Simplifying 2 + -1h = 0 Solving 2 + -1h = 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 + -1h = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1h = 0 + -2 -1h = 0 + -2 Combine like terms: 0 + -2 = -2 -1h = -2 Divide each side by '-1'. h = 2 Simplifying h = 2Subproblem 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 = {2, 2.333333333}
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