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Simplifying 16n5 + -100n3 = 0 Reorder the terms: -100n3 + 16n5 = 0 Solving -100n3 + 16n5 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4n3'. 4n3(-25 + 4n2) = 0 Factor a difference between two squares. 4n3((5 + 2n)(-5 + 2n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'n3' equal to zero and attempt to solve: Simplifying n3 = 0 Solving n3 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(5 + 2n)' equal to zero and attempt to solve: Simplifying 5 + 2n = 0 Solving 5 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2n = 0 + -5 2n = 0 + -5 Combine like terms: 0 + -5 = -5 2n = -5 Divide each side by '2'. n = -2.5 Simplifying n = -2.5Subproblem 3
Set the factor '(-5 + 2n)' equal to zero and attempt to solve: Simplifying -5 + 2n = 0 Solving -5 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 2n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2n = 0 + 5 2n = 0 + 5 Combine like terms: 0 + 5 = 5 2n = 5 Divide each side by '2'. n = 2.5 Simplifying n = 2.5Solution
n = {-2.5, 2.5}
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