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Simplifying 8n2 + 384 = 112n Reorder the terms: 384 + 8n2 = 112n Solving 384 + 8n2 = 112n Solving for variable 'n'. Reorder the terms: 384 + -112n + 8n2 = 112n + -112n Combine like terms: 112n + -112n = 0 384 + -112n + 8n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(48 + -14n + n2) = 0 Factor a trinomial. 8((6 + -1n)(8 + -1n)) = 0 Ignore the factor 8.Subproblem 1
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 = 6Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8Solution
n = {6, 8}
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