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Simplifying 2n2 + -14n = -24 Reorder the terms: -14n + 2n2 = -24 Solving -14n + 2n2 = -24 Solving for variable 'n'. Reorder the terms: 24 + -14n + 2n2 = -24 + 24 Combine like terms: -24 + 24 = 0 24 + -14n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -7n + n2) = 0 Factor a trinomial. 2((3 + -1n)(4 + -1n)) = 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 '(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 = 4Solution
n = {3, 4}
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