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Simplifying 67n2 + 120n + 31 = -5 + -8n2 Reorder the terms: 31 + 120n + 67n2 = -5 + -8n2 Solving 31 + 120n + 67n2 = -5 + -8n2 Solving for variable 'n'. Reorder the terms: 31 + 5 + 120n + 67n2 + 8n2 = -5 + -8n2 + 5 + 8n2 Combine like terms: 31 + 5 = 36 36 + 120n + 67n2 + 8n2 = -5 + -8n2 + 5 + 8n2 Combine like terms: 67n2 + 8n2 = 75n2 36 + 120n + 75n2 = -5 + -8n2 + 5 + 8n2 Reorder the terms: 36 + 120n + 75n2 = -5 + 5 + -8n2 + 8n2 Combine like terms: -5 + 5 = 0 36 + 120n + 75n2 = 0 + -8n2 + 8n2 36 + 120n + 75n2 = -8n2 + 8n2 Combine like terms: -8n2 + 8n2 = 0 36 + 120n + 75n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(12 + 40n + 25n2) = 0 Factor a trinomial. 3((6 + 5n)(2 + 5n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + 5n)' equal to zero and attempt to solve: Simplifying 6 + 5n = 0 Solving 6 + 5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 5n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5n = 0 + -6 5n = 0 + -6 Combine like terms: 0 + -6 = -6 5n = -6 Divide each side by '5'. n = -1.2 Simplifying n = -1.2Subproblem 2
Set the factor '(2 + 5n)' equal to zero and attempt to solve: Simplifying 2 + 5n = 0 Solving 2 + 5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5n = 0 + -2 5n = 0 + -2 Combine like terms: 0 + -2 = -2 5n = -2 Divide each side by '5'. n = -0.4 Simplifying n = -0.4Solution
n = {-1.2, -0.4}
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