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Simplifying 9n3 + -27n2 + -2736n = 0 Reorder the terms: -2736n + -27n2 + 9n3 = 0 Solving -2736n + -27n2 + 9n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '9n'. 9n(-304 + -3n + n2) = 0 Factor a trinomial. 9n((-16 + -1n)(19 + -1n)) = 0 Ignore the factor 9.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 '(-16 + -1n)' equal to zero and attempt to solve: Simplifying -16 + -1n = 0 Solving -16 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -1n = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1n = 0 + 16 -1n = 0 + 16 Combine like terms: 0 + 16 = 16 -1n = 16 Divide each side by '-1'. n = -16 Simplifying n = -16Subproblem 3
Set the factor '(19 + -1n)' equal to zero and attempt to solve: Simplifying 19 + -1n = 0 Solving 19 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -1n = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -1n = 0 + -19 -1n = 0 + -19 Combine like terms: 0 + -19 = -19 -1n = -19 Divide each side by '-1'. n = 19 Simplifying n = 19Solution
n = {0, -16, 19}
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