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Simplifying 18n3 + -50n = 0 Reorder the terms: -50n + 18n3 = 0 Solving -50n + 18n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2n'. 2n(-25 + 9n2) = 0 Factor a difference between two squares. 2n((5 + 3n)(-5 + 3n)) = 0 Ignore the factor 2.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 '(5 + 3n)' equal to zero and attempt to solve: Simplifying 5 + 3n = 0 Solving 5 + 3n = 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 + 3n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3n = 0 + -5 3n = 0 + -5 Combine like terms: 0 + -5 = -5 3n = -5 Divide each side by '3'. n = -1.666666667 Simplifying n = -1.666666667Subproblem 3
Set the factor '(-5 + 3n)' equal to zero and attempt to solve: Simplifying -5 + 3n = 0 Solving -5 + 3n = 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 + 3n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3n = 0 + 5 3n = 0 + 5 Combine like terms: 0 + 5 = 5 3n = 5 Divide each side by '3'. n = 1.666666667 Simplifying n = 1.666666667Solution
n = {0, -1.666666667, 1.666666667}
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