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Simplifying 24n2 = 16 + -20n Solving 24n2 = 16 + -20n Solving for variable 'n'. Reorder the terms: -16 + 20n + 24n2 = 16 + -20n + -16 + 20n Reorder the terms: -16 + 20n + 24n2 = 16 + -16 + -20n + 20n Combine like terms: 16 + -16 = 0 -16 + 20n + 24n2 = 0 + -20n + 20n -16 + 20n + 24n2 = -20n + 20n Combine like terms: -20n + 20n = 0 -16 + 20n + 24n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 5n + 6n2) = 0 Factor a trinomial. 4((-4 + -3n)(1 + -2n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + -3n)' equal to zero and attempt to solve: Simplifying -4 + -3n = 0 Solving -4 + -3n = 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 + -3n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3n = 0 + 4 -3n = 0 + 4 Combine like terms: 0 + 4 = 4 -3n = 4 Divide each side by '-3'. n = -1.333333333 Simplifying n = -1.333333333Subproblem 2
Set the factor '(1 + -2n)' equal to zero and attempt to solve: Simplifying 1 + -2n = 0 Solving 1 + -2n = 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 + -2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2n = 0 + -1 -2n = 0 + -1 Combine like terms: 0 + -1 = -1 -2n = -1 Divide each side by '-2'. n = 0.5 Simplifying n = 0.5Solution
n = {-1.333333333, 0.5}
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