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Simplifying (6n + -1)(6n + -1) + 6(6n + -1) + -112 = 0 Reorder the terms: (-1 + 6n)(6n + -1) + 6(6n + -1) + -112 = 0 Reorder the terms: (-1 + 6n)(-1 + 6n) + 6(6n + -1) + -112 = 0 Multiply (-1 + 6n) * (-1 + 6n) (-1(-1 + 6n) + 6n * (-1 + 6n)) + 6(6n + -1) + -112 = 0 ((-1 * -1 + 6n * -1) + 6n * (-1 + 6n)) + 6(6n + -1) + -112 = 0 ((1 + -6n) + 6n * (-1 + 6n)) + 6(6n + -1) + -112 = 0 (1 + -6n + (-1 * 6n + 6n * 6n)) + 6(6n + -1) + -112 = 0 (1 + -6n + (-6n + 36n2)) + 6(6n + -1) + -112 = 0 Combine like terms: -6n + -6n = -12n (1 + -12n + 36n2) + 6(6n + -1) + -112 = 0 Reorder the terms: 1 + -12n + 36n2 + 6(-1 + 6n) + -112 = 0 1 + -12n + 36n2 + (-1 * 6 + 6n * 6) + -112 = 0 1 + -12n + 36n2 + (-6 + 36n) + -112 = 0 Reorder the terms: 1 + -6 + -112 + -12n + 36n + 36n2 = 0 Combine like terms: 1 + -6 = -5 -5 + -112 + -12n + 36n + 36n2 = 0 Combine like terms: -5 + -112 = -117 -117 + -12n + 36n + 36n2 = 0 Combine like terms: -12n + 36n = 24n -117 + 24n + 36n2 = 0 Solving -117 + 24n + 36n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(-39 + 8n + 12n2) = 0 Factor a trinomial. 3((-13 + -6n)(3 + -2n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-13 + -6n)' equal to zero and attempt to solve: Simplifying -13 + -6n = 0 Solving -13 + -6n = 0 Move all terms containing n to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -6n = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -6n = 0 + 13 -6n = 0 + 13 Combine like terms: 0 + 13 = 13 -6n = 13 Divide each side by '-6'. n = -2.166666667 Simplifying n = -2.166666667Subproblem 2
Set the factor '(3 + -2n)' equal to zero and attempt to solve: Simplifying 3 + -2n = 0 Solving 3 + -2n = 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 + -2n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2n = 0 + -3 -2n = 0 + -3 Combine like terms: 0 + -3 = -3 -2n = -3 Divide each side by '-2'. n = 1.5 Simplifying n = 1.5Solution
n = {-2.166666667, 1.5}
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