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Simplifying 8n2 + -112 = -40n Reorder the terms: -112 + 8n2 = -40n Solving -112 + 8n2 = -40n Solving for variable 'n'. Reorder the terms: -112 + 40n + 8n2 = -40n + 40n Combine like terms: -40n + 40n = 0 -112 + 40n + 8n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-14 + 5n + n2) = 0 Factor a trinomial. 8((-7 + -1n)(2 + -1n)) = 0 Ignore the factor 8.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 = -7Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve: Simplifying 2 + -1n = 0 Solving 2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1n = 0 + -2 -1n = 0 + -2 Combine like terms: 0 + -2 = -2 -1n = -2 Divide each side by '-1'. n = 2 Simplifying n = 2Solution
n = {-7, 2}
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