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Simplifying 2n2 + -20n = -48 Reorder the terms: -20n + 2n2 = -48 Solving -20n + 2n2 = -48 Solving for variable 'n'. Reorder the terms: 48 + -20n + 2n2 = -48 + 48 Combine like terms: -48 + 48 = 0 48 + -20n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(24 + -10n + n2) = 0 Factor a trinomial. 2((4 + -1n)(6 + -1n)) = 0 Ignore the factor 2.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 '(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 = 6Solution
n = {4, 6}
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