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Simplifying (6h + 5)(h + -1) = -3 Reorder the terms: (5 + 6h)(h + -1) = -3 Reorder the terms: (5 + 6h)(-1 + h) = -3 Multiply (5 + 6h) * (-1 + h) (5(-1 + h) + 6h * (-1 + h)) = -3 ((-1 * 5 + h * 5) + 6h * (-1 + h)) = -3 ((-5 + 5h) + 6h * (-1 + h)) = -3 (-5 + 5h + (-1 * 6h + h * 6h)) = -3 (-5 + 5h + (-6h + 6h2)) = -3 Combine like terms: 5h + -6h = -1h (-5 + -1h + 6h2) = -3 Solving -5 + -1h + 6h2 = -3 Solving for variable 'h'. Reorder the terms: -5 + 3 + -1h + 6h2 = -3 + 3 Combine like terms: -5 + 3 = -2 -2 + -1h + 6h2 = -3 + 3 Combine like terms: -3 + 3 = 0 -2 + -1h + 6h2 = 0 Factor a trinomial. (-1 + -2h)(2 + -3h) = 0Subproblem 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 '(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 = {-0.5, 0.6666666667}
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