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Simplifying 8n2 + -46n + -12 = 0 Reorder the terms: -12 + -46n + 8n2 = 0 Solving -12 + -46n + 8n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -23n + 4n2) = 0 Factor a trinomial. 2((-1 + -4n)(6 + -1n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -4n)' equal to zero and attempt to solve: Simplifying -1 + -4n = 0 Solving -1 + -4n = 0 Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -4n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4n = 0 + 1 -4n = 0 + 1 Combine like terms: 0 + 1 = 1 -4n = 1 Divide each side by '-4'. n = -0.25 Simplifying n = -0.25Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve: Simplifying 6 + -1n = 0 Solving 6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1n = 0 + -6 -1n = 0 + -6 Combine like terms: 0 + -6 = -6 -1n = -6 Divide each side by '-1'. n = 6 Simplifying n = 6Solution
n = {-0.25, 6}
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