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Simplifying 48n2 + 276n + 378 = 0 Reorder the terms: 378 + 276n + 48n2 = 0 Solving 378 + 276n + 48n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '6'. 6(63 + 46n + 8n2) = 0 Factor a trinomial. 6((7 + 2n)(9 + 4n)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(7 + 2n)' equal to zero and attempt to solve: Simplifying 7 + 2n = 0 Solving 7 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2n = 0 + -7 2n = 0 + -7 Combine like terms: 0 + -7 = -7 2n = -7 Divide each side by '2'. n = -3.5 Simplifying n = -3.5Subproblem 2
Set the factor '(9 + 4n)' equal to zero and attempt to solve: Simplifying 9 + 4n = 0 Solving 9 + 4n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4n = 0 + -9 4n = 0 + -9 Combine like terms: 0 + -9 = -9 4n = -9 Divide each side by '4'. n = -2.25 Simplifying n = -2.25Solution
n = {-3.5, -2.25}
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