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Simplifying 8n3 + -24n2 + -3680n = 0 Reorder the terms: -3680n + -24n2 + 8n3 = 0 Solving -3680n + -24n2 + 8n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '8n'. 8n(-460 + -3n + n2) = 0 Factor a trinomial. 8n((-20 + -1n)(23 + -1n)) = 0 Ignore the factor 8.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 '(-20 + -1n)' equal to zero and attempt to solve: Simplifying -20 + -1n = 0 Solving -20 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + -1n = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -1n = 0 + 20 -1n = 0 + 20 Combine like terms: 0 + 20 = 20 -1n = 20 Divide each side by '-1'. n = -20 Simplifying n = -20Subproblem 3
Set the factor '(23 + -1n)' equal to zero and attempt to solve: Simplifying 23 + -1n = 0 Solving 23 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + -1n = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -1n = 0 + -23 -1n = 0 + -23 Combine like terms: 0 + -23 = -23 -1n = -23 Divide each side by '-1'. n = 23 Simplifying n = 23Solution
n = {0, -20, 23}
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