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Simplifying 6n2 = 10n + 136 Reorder the terms: 6n2 = 136 + 10n Solving 6n2 = 136 + 10n Solving for variable 'n'. Reorder the terms: -136 + -10n + 6n2 = 136 + 10n + -136 + -10n Reorder the terms: -136 + -10n + 6n2 = 136 + -136 + 10n + -10n Combine like terms: 136 + -136 = 0 -136 + -10n + 6n2 = 0 + 10n + -10n -136 + -10n + 6n2 = 10n + -10n Combine like terms: 10n + -10n = 0 -136 + -10n + 6n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-68 + -5n + 3n2) = 0 Factor a trinomial. 2((-4 + -1n)(17 + -3n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve: Simplifying -4 + -1n = 0 Solving -4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1n = 0 + 4 -1n = 0 + 4 Combine like terms: 0 + 4 = 4 -1n = 4 Divide each side by '-1'. n = -4 Simplifying n = -4Subproblem 2
Set the factor '(17 + -3n)' equal to zero and attempt to solve: Simplifying 17 + -3n = 0 Solving 17 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -3n = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -3n = 0 + -17 -3n = 0 + -17 Combine like terms: 0 + -17 = -17 -3n = -17 Divide each side by '-3'. n = 5.666666667 Simplifying n = 5.666666667Solution
n = {-4, 5.666666667}
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