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Simplifying 0 = 6n2 + 24n + -840 Reorder the terms: 0 = -840 + 24n + 6n2 Solving 0 = -840 + 24n + 6n2 Solving for variable 'n'. Combine like terms: 0 + 840 = 840 840 + -24n + -6n2 = -840 + 24n + 6n2 + 840 + -24n + -6n2 Reorder the terms: 840 + -24n + -6n2 = -840 + 840 + 24n + -24n + 6n2 + -6n2 Combine like terms: -840 + 840 = 0 840 + -24n + -6n2 = 0 + 24n + -24n + 6n2 + -6n2 840 + -24n + -6n2 = 24n + -24n + 6n2 + -6n2 Combine like terms: 24n + -24n = 0 840 + -24n + -6n2 = 0 + 6n2 + -6n2 840 + -24n + -6n2 = 6n2 + -6n2 Combine like terms: 6n2 + -6n2 = 0 840 + -24n + -6n2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(140 + -4n + -1n2) = 0 Factor a trinomial. 6((10 + -1n)(14 + n)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(10 + -1n)' equal to zero and attempt to solve: Simplifying 10 + -1n = 0 Solving 10 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1n = 0 + -10 -1n = 0 + -10 Combine like terms: 0 + -10 = -10 -1n = -10 Divide each side by '-1'. n = 10 Simplifying n = 10Subproblem 2
Set the factor '(14 + n)' equal to zero and attempt to solve: Simplifying 14 + n = 0 Solving 14 + n = 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 + n = 0 + -14 Combine like terms: 14 + -14 = 0 0 + n = 0 + -14 n = 0 + -14 Combine like terms: 0 + -14 = -14 n = -14 Simplifying n = -14Solution
n = {10, -14}
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