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Simplifying 0 = 4n3 + -11n2 + -20n Reorder the terms: 0 = -20n + -11n2 + 4n3 Solving 0 = -20n + -11n2 + 4n3 Solving for variable 'n'. Remove the zero: 20n + 11n2 + -4n3 = -20n + -11n2 + 4n3 + 20n + 11n2 + -4n3 Reorder the terms: 20n + 11n2 + -4n3 = -20n + 20n + -11n2 + 11n2 + 4n3 + -4n3 Combine like terms: -20n + 20n = 0 20n + 11n2 + -4n3 = 0 + -11n2 + 11n2 + 4n3 + -4n3 20n + 11n2 + -4n3 = -11n2 + 11n2 + 4n3 + -4n3 Combine like terms: -11n2 + 11n2 = 0 20n + 11n2 + -4n3 = 0 + 4n3 + -4n3 20n + 11n2 + -4n3 = 4n3 + -4n3 Combine like terms: 4n3 + -4n3 = 0 20n + 11n2 + -4n3 = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(20 + 11n + -4n2) = 0 Factor a trinomial. n((4 + -1n)(5 + 4n)) = 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 '(5 + 4n)' equal to zero and attempt to solve: Simplifying 5 + 4n = 0 Solving 5 + 4n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4n = 0 + -5 4n = 0 + -5 Combine like terms: 0 + -5 = -5 4n = -5 Divide each side by '4'. n = -1.25 Simplifying n = -1.25Solution
n = {0, 4, -1.25}
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