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Simplifying h(3h + -4)(h + 1) = 0 Reorder the terms: h(-4 + 3h)(h + 1) = 0 Reorder the terms: h(-4 + 3h)(1 + h) = 0 Multiply (-4 + 3h) * (1 + h) h(-4(1 + h) + 3h * (1 + h)) = 0 h((1 * -4 + h * -4) + 3h * (1 + h)) = 0 h((-4 + -4h) + 3h * (1 + h)) = 0 h(-4 + -4h + (1 * 3h + h * 3h)) = 0 h(-4 + -4h + (3h + 3h2)) = 0 Combine like terms: -4h + 3h = -1h h(-4 + -1h + 3h2) = 0 (-4 * h + -1h * h + 3h2 * h) = 0 (-4h + -1h2 + 3h3) = 0 Solving -4h + -1h2 + 3h3 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), 'h'. h(-4 + -1h + 3h2) = 0 Factor a trinomial. h((-1 + -1h)(4 + -3h)) = 0Subproblem 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 '(-1 + -1h)' equal to zero and attempt to solve: Simplifying -1 + -1h = 0 Solving -1 + -1h = 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 + -1h = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1h = 0 + 1 -1h = 0 + 1 Combine like terms: 0 + 1 = 1 -1h = 1 Divide each side by '-1'. h = -1 Simplifying h = -1Subproblem 3
Set the factor '(4 + -3h)' equal to zero and attempt to solve: Simplifying 4 + -3h = 0 Solving 4 + -3h = 0 Move all terms containing h to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3h = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3h = 0 + -4 -3h = 0 + -4 Combine like terms: 0 + -4 = -4 -3h = -4 Divide each side by '-3'. h = 1.333333333 Simplifying h = 1.333333333Solution
h = {0, -1, 1.333333333}
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