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Simplifying 9n3 + 28n2 + -32n = 0 Reorder the terms: -32n + 28n2 + 9n3 = 0 Solving -32n + 28n2 + 9n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(-32 + 28n + 9n2) = 0 Factor a trinomial. n((-4 + -1n)(8 + -9n)) = 0Subproblem 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 '(-4 + -1n)' equal to zero and attempt to solve: Simplifying -4 + -1n = 0 Solving -4 + -1n = 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 + -1n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1n = 0 + 4 -1n = 0 + 4 Combine like terms: 0 + 4 = 4 -1n = 4 Divide each side by '-1'. n = -4 Simplifying n = -4Subproblem 3
Set the factor '(8 + -9n)' equal to zero and attempt to solve: Simplifying 8 + -9n = 0 Solving 8 + -9n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -9n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -9n = 0 + -8 -9n = 0 + -8 Combine like terms: 0 + -8 = -8 -9n = -8 Divide each side by '-9'. n = 0.8888888889 Simplifying n = 0.8888888889Solution
n = {0, -4, 0.8888888889}
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