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Simplifying 4n3 + -31n2 + -90n = 0 Reorder the terms: -90n + -31n2 + 4n3 = 0 Solving -90n + -31n2 + 4n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(-90 + -31n + 4n2) = 0 Factor a trinomial. n((-9 + -4n)(10 + -1n)) = 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 '(-9 + -4n)' equal to zero and attempt to solve: Simplifying -9 + -4n = 0 Solving -9 + -4n = 0 Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -4n = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4n = 0 + 9 -4n = 0 + 9 Combine like terms: 0 + 9 = 9 -4n = 9 Divide each side by '-4'. n = -2.25 Simplifying n = -2.25Subproblem 3
Set the factor '(10 + -1n)' equal to zero and attempt to solve: Simplifying 10 + -1n = 0 Solving 10 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1n = 0 + -10 -1n = 0 + -10 Combine like terms: 0 + -10 = -10 -1n = -10 Divide each side by '-1'. n = 10 Simplifying n = 10Solution
n = {0, -2.25, 10}
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