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Simplifying 9n2 = -192 + 96n Solving 9n2 = -192 + 96n Solving for variable 'n'. Reorder the terms: 192 + -96n + 9n2 = -192 + 96n + 192 + -96n Reorder the terms: 192 + -96n + 9n2 = -192 + 192 + 96n + -96n Combine like terms: -192 + 192 = 0 192 + -96n + 9n2 = 0 + 96n + -96n 192 + -96n + 9n2 = 96n + -96n Combine like terms: 96n + -96n = 0 192 + -96n + 9n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(64 + -32n + 3n2) = 0 Factor a trinomial. 3((8 + -3n)(8 + -1n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8 + -3n)' equal to zero and attempt to solve: Simplifying 8 + -3n = 0 Solving 8 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3n = 0 + -8 -3n = 0 + -8 Combine like terms: 0 + -8 = -8 -3n = -8 Divide each side by '-3'. n = 2.666666667 Simplifying n = 2.666666667Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8Solution
n = {2.666666667, 8}
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