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Simplifying 24n2 + -320 = 152n Reorder the terms: -320 + 24n2 = 152n Solving -320 + 24n2 = 152n Solving for variable 'n'. Reorder the terms: -320 + -152n + 24n2 = 152n + -152n Combine like terms: 152n + -152n = 0 -320 + -152n + 24n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-40 + -19n + 3n2) = 0 Factor a trinomial. 8((-5 + -3n)(8 + -1n)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-5 + -3n)' equal to zero and attempt to solve: Simplifying -5 + -3n = 0 Solving -5 + -3n = 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 + -3n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3n = 0 + 5 -3n = 0 + 5 Combine like terms: 0 + 5 = 5 -3n = 5 Divide each side by '-3'. n = -1.666666667 Simplifying n = -1.666666667Subproblem 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 = {-1.666666667, 8}
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