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Simplifying 15n2 = 24n + -9 Reorder the terms: 15n2 = -9 + 24n Solving 15n2 = -9 + 24n Solving for variable 'n'. Reorder the terms: 9 + -24n + 15n2 = -9 + 24n + 9 + -24n Reorder the terms: 9 + -24n + 15n2 = -9 + 9 + 24n + -24n Combine like terms: -9 + 9 = 0 9 + -24n + 15n2 = 0 + 24n + -24n 9 + -24n + 15n2 = 24n + -24n Combine like terms: 24n + -24n = 0 9 + -24n + 15n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -8n + 5n2) = 0 Factor a trinomial. 3((3 + -5n)(1 + -1n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -5n)' equal to zero and attempt to solve: Simplifying 3 + -5n = 0 Solving 3 + -5n = 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 + -5n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5n = 0 + -3 -5n = 0 + -3 Combine like terms: 0 + -3 = -3 -5n = -3 Divide each side by '-5'. n = 0.6 Simplifying n = 0.6Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Solution
n = {0.6, 1}
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