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Simplifying 54n2 + 193n = -2n2 + -72 + n Reorder the terms: 193n + 54n2 = -2n2 + -72 + n Reorder the terms: 193n + 54n2 = -72 + n + -2n2 Solving 193n + 54n2 = -72 + n + -2n2 Solving for variable 'n'. Reorder the terms: 72 + 193n + -1n + 54n2 + 2n2 = -72 + n + -2n2 + 72 + -1n + 2n2 Combine like terms: 193n + -1n = 192n 72 + 192n + 54n2 + 2n2 = -72 + n + -2n2 + 72 + -1n + 2n2 Combine like terms: 54n2 + 2n2 = 56n2 72 + 192n + 56n2 = -72 + n + -2n2 + 72 + -1n + 2n2 Reorder the terms: 72 + 192n + 56n2 = -72 + 72 + n + -1n + -2n2 + 2n2 Combine like terms: -72 + 72 = 0 72 + 192n + 56n2 = 0 + n + -1n + -2n2 + 2n2 72 + 192n + 56n2 = n + -1n + -2n2 + 2n2 Combine like terms: n + -1n = 0 72 + 192n + 56n2 = 0 + -2n2 + 2n2 72 + 192n + 56n2 = -2n2 + 2n2 Combine like terms: -2n2 + 2n2 = 0 72 + 192n + 56n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(9 + 24n + 7n2) = 0 Factor a trinomial. 8((3 + n)(3 + 7n)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(3 + n)' equal to zero and attempt to solve: Simplifying 3 + n = 0 Solving 3 + n = 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 + n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + n = 0 + -3 n = 0 + -3 Combine like terms: 0 + -3 = -3 n = -3 Simplifying n = -3Subproblem 2
Set the factor '(3 + 7n)' equal to zero and attempt to solve: Simplifying 3 + 7n = 0 Solving 3 + 7n = 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 + 7n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7n = 0 + -3 7n = 0 + -3 Combine like terms: 0 + -3 = -3 7n = -3 Divide each side by '7'. n = -0.4285714286 Simplifying n = -0.4285714286Solution
n = {-3, -0.4285714286}
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