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Simplifying (5h + 1)(4h + -7) = 0 Reorder the terms: (1 + 5h)(4h + -7) = 0 Reorder the terms: (1 + 5h)(-7 + 4h) = 0 Multiply (1 + 5h) * (-7 + 4h) (1(-7 + 4h) + 5h * (-7 + 4h)) = 0 ((-7 * 1 + 4h * 1) + 5h * (-7 + 4h)) = 0 ((-7 + 4h) + 5h * (-7 + 4h)) = 0 (-7 + 4h + (-7 * 5h + 4h * 5h)) = 0 (-7 + 4h + (-35h + 20h2)) = 0 Combine like terms: 4h + -35h = -31h (-7 + -31h + 20h2) = 0 Solving -7 + -31h + 20h2 = 0 Solving for variable 'h'. Factor a trinomial. (-1 + -5h)(7 + -4h) = 0Subproblem 1
Set the factor '(-1 + -5h)' equal to zero and attempt to solve: Simplifying -1 + -5h = 0 Solving -1 + -5h = 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 + -5h = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5h = 0 + 1 -5h = 0 + 1 Combine like terms: 0 + 1 = 1 -5h = 1 Divide each side by '-5'. h = -0.2 Simplifying h = -0.2Subproblem 2
Set the factor '(7 + -4h)' equal to zero and attempt to solve: Simplifying 7 + -4h = 0 Solving 7 + -4h = 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 + -4h = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4h = 0 + -7 -4h = 0 + -7 Combine like terms: 0 + -7 = -7 -4h = -7 Divide each side by '-4'. h = 1.75 Simplifying h = 1.75Solution
h = {-0.2, 1.75}
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