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Simplifying 4n2 = 48 + -4n Solving 4n2 = 48 + -4n Solving for variable 'n'. Reorder the terms: -48 + 4n + 4n2 = 48 + -4n + -48 + 4n Reorder the terms: -48 + 4n + 4n2 = 48 + -48 + -4n + 4n Combine like terms: 48 + -48 = 0 -48 + 4n + 4n2 = 0 + -4n + 4n -48 + 4n + 4n2 = -4n + 4n Combine like terms: -4n + 4n = 0 -48 + 4n + 4n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-12 + n + n2) = 0 Factor a trinomial. 4((-4 + -1n)(3 + -1n)) = 0 Ignore the factor 4.Subproblem 1
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 = -4Subproblem 2
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 = 3Solution
n = {-4, 3}
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