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Simplifying 8n2 = 48 + -8n Solving 8n2 = 48 + -8n Solving for variable 'n'. Reorder the terms: -48 + 8n + 8n2 = 48 + -8n + -48 + 8n Reorder the terms: -48 + 8n + 8n2 = 48 + -48 + -8n + 8n Combine like terms: 48 + -48 = 0 -48 + 8n + 8n2 = 0 + -8n + 8n -48 + 8n + 8n2 = -8n + 8n Combine like terms: -8n + 8n = 0 -48 + 8n + 8n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-6 + n + n2) = 0 Factor a trinomial. 8((-3 + -1n)(2 + -1n)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve: Simplifying -3 + -1n = 0 Solving -3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n = 0 + 3 -1n = 0 + 3 Combine like terms: 0 + 3 = 3 -1n = 3 Divide each side by '-1'. n = -3 Simplifying n = -3Subproblem 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 = {-3, 2}
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