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Simplifying (5h + -3)(h + 7) = 0 Reorder the terms: (-3 + 5h)(h + 7) = 0 Reorder the terms: (-3 + 5h)(7 + h) = 0 Multiply (-3 + 5h) * (7 + h) (-3(7 + h) + 5h * (7 + h)) = 0 ((7 * -3 + h * -3) + 5h * (7 + h)) = 0 ((-21 + -3h) + 5h * (7 + h)) = 0 (-21 + -3h + (7 * 5h + h * 5h)) = 0 (-21 + -3h + (35h + 5h2)) = 0 Combine like terms: -3h + 35h = 32h (-21 + 32h + 5h2) = 0 Solving -21 + 32h + 5h2 = 0 Solving for variable 'h'. Factor a trinomial. (-7 + -1h)(3 + -5h) = 0Subproblem 1
Set the factor '(-7 + -1h)' equal to zero and attempt to solve: Simplifying -7 + -1h = 0 Solving -7 + -1h = 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 + -1h = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1h = 0 + 7 -1h = 0 + 7 Combine like terms: 0 + 7 = 7 -1h = 7 Divide each side by '-1'. h = -7 Simplifying h = -7Subproblem 2
Set the factor '(3 + -5h)' equal to zero and attempt to solve: Simplifying 3 + -5h = 0 Solving 3 + -5h = 0 Move all terms containing h to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5h = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5h = 0 + -3 -5h = 0 + -3 Combine like terms: 0 + -3 = -3 -5h = -3 Divide each side by '-5'. h = 0.6 Simplifying h = 0.6Solution
h = {-7, 0.6}
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