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Simplifying 6n2 + 10n + -84 = 0 Reorder the terms: -84 + 10n + 6n2 = 0 Solving -84 + 10n + 6n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-42 + 5n + 3n2) = 0 Factor a trinomial. 2((-14 + -3n)(3 + -1n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-14 + -3n)' equal to zero and attempt to solve: Simplifying -14 + -3n = 0 Solving -14 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -3n = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -3n = 0 + 14 -3n = 0 + 14 Combine like terms: 0 + 14 = 14 -3n = 14 Divide each side by '-3'. n = -4.666666667 Simplifying n = -4.666666667Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve: Simplifying 3 + -1n = 0 Solving 3 + -1n = 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 + -1n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1n = 0 + -3 -1n = 0 + -3 Combine like terms: 0 + -3 = -3 -1n = -3 Divide each side by '-1'. n = 3 Simplifying n = 3Solution
n = {-4.666666667, 3}
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