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Simplifying 75h4 + 60h3 + 12h2 = 0 Reorder the terms: 12h2 + 60h3 + 75h4 = 0 Solving 12h2 + 60h3 + 75h4 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '3h2'. 3h2(4 + 20h + 25h2) = 0 Factor a trinomial. 3h2((2 + 5h)(2 + 5h)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'h2' equal to zero and attempt to solve: Simplifying h2 = 0 Solving h2 = 0 Move all terms containing h to the left, all other terms to the right. Simplifying h2 = 0 Take the square root of each side: h = {0}Subproblem 2
Set the factor '(2 + 5h)' equal to zero and attempt to solve: Simplifying 2 + 5h = 0 Solving 2 + 5h = 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 + 5h = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5h = 0 + -2 5h = 0 + -2 Combine like terms: 0 + -2 = -2 5h = -2 Divide each side by '5'. h = -0.4 Simplifying h = -0.4Subproblem 3
Set the factor '(2 + 5h)' equal to zero and attempt to solve: Simplifying 2 + 5h = 0 Solving 2 + 5h = 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 + 5h = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5h = 0 + -2 5h = 0 + -2 Combine like terms: 0 + -2 = -2 5h = -2 Divide each side by '5'. h = -0.4 Simplifying h = -0.4Solution
h = {0, -0.4, -0.4}
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