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Simplifying 4h(3h + -2)(h + 6) = 0 Reorder the terms: 4h(-2 + 3h)(h + 6) = 0 Reorder the terms: 4h(-2 + 3h)(6 + h) = 0 Multiply (-2 + 3h) * (6 + h) 4h(-2(6 + h) + 3h * (6 + h)) = 0 4h((6 * -2 + h * -2) + 3h * (6 + h)) = 0 4h((-12 + -2h) + 3h * (6 + h)) = 0 4h(-12 + -2h + (6 * 3h + h * 3h)) = 0 4h(-12 + -2h + (18h + 3h2)) = 0 Combine like terms: -2h + 18h = 16h 4h(-12 + 16h + 3h2) = 0 (-12 * 4h + 16h * 4h + 3h2 * 4h) = 0 (-48h + 64h2 + 12h3) = 0 Solving -48h + 64h2 + 12h3 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '4h'. 4h(-12 + 16h + 3h2) = 0 Factor a trinomial. 4h((-6 + -1h)(2 + -3h)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'h' equal to zero and attempt to solve: Simplifying h = 0 Solving h = 0 Move all terms containing h to the left, all other terms to the right. Simplifying h = 0Subproblem 2
Set the factor '(-6 + -1h)' equal to zero and attempt to solve: Simplifying -6 + -1h = 0 Solving -6 + -1h = 0 Move all terms containing h to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1h = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1h = 0 + 6 -1h = 0 + 6 Combine like terms: 0 + 6 = 6 -1h = 6 Divide each side by '-1'. h = -6 Simplifying h = -6Subproblem 3
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, -6, 0.6666666667}
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