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Simplifying 15n5 + -72n3 + -108n = 0 Reorder the terms: -108n + -72n3 + 15n5 = 0 Solving -108n + -72n3 + 15n5 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3n'. 3n(-36 + -24n2 + 5n4) = 0 Factor a trinomial. 3n((-6 + -5n2)(6 + -1n2)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(-6 + -5n2)' equal to zero and attempt to solve: Simplifying -6 + -5n2 = 0 Solving -6 + -5n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -5n2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5n2 = 0 + 6 -5n2 = 0 + 6 Combine like terms: 0 + 6 = 6 -5n2 = 6 Divide each side by '-5'. n2 = -1.2 Simplifying n2 = -1.2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(6 + -1n2)' equal to zero and attempt to solve: Simplifying 6 + -1n2 = 0 Solving 6 + -1n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1n2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1n2 = 0 + -6 -1n2 = 0 + -6 Combine like terms: 0 + -6 = -6 -1n2 = -6 Divide each side by '-1'. n2 = 6 Simplifying n2 = 6 Take the square root of each side: n = {-2.449489743, 2.449489743}Solution
n = {0, -2.449489743, 2.449489743}
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