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Simplifying (2h + 3)(h + -4) = 13 Reorder the terms: (3 + 2h)(h + -4) = 13 Reorder the terms: (3 + 2h)(-4 + h) = 13 Multiply (3 + 2h) * (-4 + h) (3(-4 + h) + 2h * (-4 + h)) = 13 ((-4 * 3 + h * 3) + 2h * (-4 + h)) = 13 ((-12 + 3h) + 2h * (-4 + h)) = 13 (-12 + 3h + (-4 * 2h + h * 2h)) = 13 (-12 + 3h + (-8h + 2h2)) = 13 Combine like terms: 3h + -8h = -5h (-12 + -5h + 2h2) = 13 Solving -12 + -5h + 2h2 = 13 Solving for variable 'h'. Reorder the terms: -12 + -13 + -5h + 2h2 = 13 + -13 Combine like terms: -12 + -13 = -25 -25 + -5h + 2h2 = 13 + -13 Combine like terms: 13 + -13 = 0 -25 + -5h + 2h2 = 0 Factor a trinomial. (-5 + -2h)(5 + -1h) = 0Subproblem 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 '(5 + -1h)' equal to zero and attempt to solve: Simplifying 5 + -1h = 0 Solving 5 + -1h = 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 + -1h = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1h = 0 + -5 -1h = 0 + -5 Combine like terms: 0 + -5 = -5 -1h = -5 Divide each side by '-1'. h = 5 Simplifying h = 5Solution
h = {-2.5, 5}
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