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Simplifying 30h4 + 25h3 + -5h2 = 0 Reorder the terms: -5h2 + 25h3 + 30h4 = 0 Solving -5h2 + 25h3 + 30h4 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '5h2'. 5h2(-1 + 5h + 6h2) = 0 Factor a trinomial. 5h2((-1 + -1h)(1 + -6h)) = 0 Ignore the factor 5.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 '(-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 '(1 + -6h)' equal to zero and attempt to solve: Simplifying 1 + -6h = 0 Solving 1 + -6h = 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 + -6h = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6h = 0 + -1 -6h = 0 + -1 Combine like terms: 0 + -1 = -1 -6h = -1 Divide each side by '-6'. h = 0.1666666667 Simplifying h = 0.1666666667Solution
h = {0, -1, 0.1666666667}
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