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Simplifying 30n3 + 5n2 + -60n = 0 Reorder the terms: -60n + 5n2 + 30n3 = 0 Solving -60n + 5n2 + 30n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '5n'. 5n(-12 + n + 6n2) = 0 Factor a trinomial. 5n((-3 + -2n)(4 + -3n)) = 0 Ignore the factor 5.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 '(-3 + -2n)' equal to zero and attempt to solve: Simplifying -3 + -2n = 0 Solving -3 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2n = 0 + 3 -2n = 0 + 3 Combine like terms: 0 + 3 = 3 -2n = 3 Divide each side by '-2'. n = -1.5 Simplifying n = -1.5Subproblem 3
Set the factor '(4 + -3n)' equal to zero and attempt to solve: Simplifying 4 + -3n = 0 Solving 4 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3n = 0 + -4 -3n = 0 + -4 Combine like terms: 0 + -4 = -4 -3n = -4 Divide each side by '-3'. n = 1.333333333 Simplifying n = 1.333333333Solution
n = {0, -1.5, 1.333333333}
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