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Simplifying 104n2 = 20n3 + 96n Reorder the terms: 104n2 = 96n + 20n3 Solving 104n2 = 96n + 20n3 Solving for variable 'n'. Reorder the terms: -96n + 104n2 + -20n3 = 96n + 20n3 + -96n + -20n3 Reorder the terms: -96n + 104n2 + -20n3 = 96n + -96n + 20n3 + -20n3 Combine like terms: 96n + -96n = 0 -96n + 104n2 + -20n3 = 0 + 20n3 + -20n3 -96n + 104n2 + -20n3 = 20n3 + -20n3 Combine like terms: 20n3 + -20n3 = 0 -96n + 104n2 + -20n3 = 0 Factor out the Greatest Common Factor (GCF), '4n'. 4n(-24 + 26n + -5n2) = 0 Factor a trinomial. 4n((-4 + n)(6 + -5n)) = 0 Ignore the factor 4.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 '(-4 + n)' equal to zero and attempt to solve: Simplifying -4 + n = 0 Solving -4 + n = 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 + n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + n = 0 + 4 n = 0 + 4 Combine like terms: 0 + 4 = 4 n = 4 Simplifying n = 4Subproblem 3
Set the factor '(6 + -5n)' equal to zero and attempt to solve: Simplifying 6 + -5n = 0 Solving 6 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5n = 0 + -6 -5n = 0 + -6 Combine like terms: 0 + -6 = -6 -5n = -6 Divide each side by '-5'. n = 1.2 Simplifying n = 1.2Solution
n = {0, 4, 1.2}
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