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Simplifying 3n3 + -37n2 + 90n = 0 Reorder the terms: 90n + -37n2 + 3n3 = 0 Solving 90n + -37n2 + 3n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(90 + -37n + 3n2) = 0 Factor a trinomial. n((10 + -3n)(9 + -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 '(10 + -3n)' equal to zero and attempt to solve: Simplifying 10 + -3n = 0 Solving 10 + -3n = 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 + -3n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3n = 0 + -10 -3n = 0 + -10 Combine like terms: 0 + -10 = -10 -3n = -10 Divide each side by '-3'. n = 3.333333333 Simplifying n = 3.333333333Subproblem 3
Set the factor '(9 + -1n)' equal to zero and attempt to solve: Simplifying 9 + -1n = 0 Solving 9 + -1n = 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 + -1n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1n = 0 + -9 -1n = 0 + -9 Combine like terms: 0 + -9 = -9 -1n = -9 Divide each side by '-1'. n = 9 Simplifying n = 9Solution
n = {0, 3.333333333, 9}
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