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Simplifying 6n2 + -128 = -8n Reorder the terms: -128 + 6n2 = -8n Solving -128 + 6n2 = -8n Solving for variable 'n'. Reorder the terms: -128 + 8n + 6n2 = -8n + 8n Combine like terms: -8n + 8n = 0 -128 + 8n + 6n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-64 + 4n + 3n2) = 0 Factor a trinomial. 2((-16 + -3n)(4 + -1n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + -3n)' equal to zero and attempt to solve: Simplifying -16 + -3n = 0 Solving -16 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -3n = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -3n = 0 + 16 -3n = 0 + 16 Combine like terms: 0 + 16 = 16 -3n = 16 Divide each side by '-3'. n = -5.333333333 Simplifying n = -5.333333333Subproblem 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 = {-5.333333333, 4}
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