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Simplifying 16h5 + -25h3 + 9h = 0 Reorder the terms: 9h + -25h3 + 16h5 = 0 Solving 9h + -25h3 + 16h5 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), 'h'. h(9 + -25h2 + 16h4) = 0 Factor a trinomial. h((9 + -16h2)(1 + -1h2)) = 0 Factor a difference between two squares. h(((3 + 4h)(3 + -4h))(1 + -1h2)) = 0 Factor a difference between two squares. h(((1 + h)(1 + -1h))(3 + 4h)(3 + -4h)) = 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 '(3 + 4h)' equal to zero and attempt to solve: Simplifying 3 + 4h = 0 Solving 3 + 4h = 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 + 4h = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4h = 0 + -3 4h = 0 + -3 Combine like terms: 0 + -3 = -3 4h = -3 Divide each side by '4'. h = -0.75 Simplifying h = -0.75Subproblem 3
Set the factor '(3 + -4h)' equal to zero and attempt to solve: Simplifying 3 + -4h = 0 Solving 3 + -4h = 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 + -4h = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4h = 0 + -3 -4h = 0 + -3 Combine like terms: 0 + -3 = -3 -4h = -3 Divide each side by '-4'. h = 0.75 Simplifying h = 0.75Subproblem 4
Set the factor '(1 + h)' equal to zero and attempt to solve: Simplifying 1 + h = 0 Solving 1 + h = 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 + h = 0 + -1 Combine like terms: 1 + -1 = 0 0 + h = 0 + -1 h = 0 + -1 Combine like terms: 0 + -1 = -1 h = -1 Simplifying h = -1Subproblem 5
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 = 1Solution
h = {0, -0.75, 0.75, -1, 1}
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