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Simplifying -8n2 + 24n + -16 = 0 Reorder the terms: -16 + 24n + -8n2 = 0 Solving -16 + 24n + -8n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '8'. 8(-2 + 3n + -1n2) = 0 Factor a trinomial. 8((-2 + n)(1 + -1n)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-2 + n)' equal to zero and attempt to solve: Simplifying -2 + n = 0 Solving -2 + n = 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 + n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + n = 0 + 2 n = 0 + 2 Combine like terms: 0 + 2 = 2 n = 2 Simplifying n = 2Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 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 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Solution
n = {2, 1}
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