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Simplifying 8n7 + -80n6 + -312n5 = 0 Reorder the terms: -312n5 + -80n6 + 8n7 = 0 Solving -312n5 + -80n6 + 8n7 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '8n5'. 8n5(-39 + -10n + n2) = 0 Factor a trinomial. 8n5((-3 + -1n)(13 + -1n)) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'n5' equal to zero and attempt to solve: Simplifying n5 = 0 Solving n5 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n5 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-3 + -1n)' equal to zero and attempt to solve: Simplifying -3 + -1n = 0 Solving -3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n = 0 + 3 -1n = 0 + 3 Combine like terms: 0 + 3 = 3 -1n = 3 Divide each side by '-1'. n = -3 Simplifying n = -3Subproblem 3
Set the factor '(13 + -1n)' equal to zero and attempt to solve: Simplifying 13 + -1n = 0 Solving 13 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1n = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1n = 0 + -13 -1n = 0 + -13 Combine like terms: 0 + -13 = -13 -1n = -13 Divide each side by '-1'. n = 13 Simplifying n = 13Solution
n = {-3, 13}
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