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Simplifying 6n2 + -10n = 84 Reorder the terms: -10n + 6n2 = 84 Solving -10n + 6n2 = 84 Solving for variable 'n'. Reorder the terms: -84 + -10n + 6n2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + -10n + 6n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-42 + -5n + 3n2) = 0 Factor a trinomial. 2((-3 + -1n)(14 + -3n)) = 0 Ignore the factor 2.Subproblem 1
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 = -3Subproblem 2
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 = 4.666666667Solution
n = {-3, 4.666666667}
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