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Simplifying 72n2 + -15n + -3 = 0 Reorder the terms: -3 + -15n + 72n2 = 0 Solving -3 + -15n + 72n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -5n + 24n2) = 0 Factor a trinomial. 3((-1 + -8n)(1 + -3n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -8n)' equal to zero and attempt to solve: Simplifying -1 + -8n = 0 Solving -1 + -8n = 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 + -8n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8n = 0 + 1 -8n = 0 + 1 Combine like terms: 0 + 1 = 1 -8n = 1 Divide each side by '-8'. n = -0.125 Simplifying n = -0.125Subproblem 2
Set the factor '(1 + -3n)' equal to zero and attempt to solve: Simplifying 1 + -3n = 0 Solving 1 + -3n = 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 + -3n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3n = 0 + -1 -3n = 0 + -1 Combine like terms: 0 + -1 = -1 -3n = -1 Divide each side by '-3'. n = 0.3333333333 Simplifying n = 0.3333333333Solution
n = {-0.125, 0.3333333333}
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