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Simplifying 2n^{2}+ 8n + -42 = 0 Reorder the terms: -42 + 8n + 2n^{2}= 0 Solving -42 + 8n + 2n^{2}= 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 4n + n^{2}) = 0 Factor a trinomial. 2((-7 + -1n)(3 + -1n)) = 0 Ignore the factor 2.## Subproblem 1

Set the factor '(-7 + -1n)' equal to zero and attempt to solve: Simplifying -7 + -1n = 0 Solving -7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1n = 0 + 7 -1n = 0 + 7 Combine like terms: 0 + 7 = 7 -1n = 7 Divide each side by '-1'. n = -7 Simplifying n = -7## Subproblem 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 = 3## Solution

n = {-7, 3}

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