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Simplifying 6n2 + -18n + -68 = -8 Reorder the terms: -68 + -18n + 6n2 = -8 Solving -68 + -18n + 6n2 = -8 Solving for variable 'n'. Reorder the terms: -68 + 8 + -18n + 6n2 = -8 + 8 Combine like terms: -68 + 8 = -60 -60 + -18n + 6n2 = -8 + 8 Combine like terms: -8 + 8 = 0 -60 + -18n + 6n2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-10 + -3n + n2) = 0 Factor a trinomial. 6((-2 + -1n)(5 + -1n)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 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 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 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 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Solution
n = {-2, 5}
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