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Simplifying 16n2 + 23n = -12 + 11n2 Reorder the terms: 23n + 16n2 = -12 + 11n2 Solving 23n + 16n2 = -12 + 11n2 Solving for variable 'n'. Reorder the terms: 12 + 23n + 16n2 + -11n2 = -12 + 11n2 + 12 + -11n2 Combine like terms: 16n2 + -11n2 = 5n2 12 + 23n + 5n2 = -12 + 11n2 + 12 + -11n2 Reorder the terms: 12 + 23n + 5n2 = -12 + 12 + 11n2 + -11n2 Combine like terms: -12 + 12 = 0 12 + 23n + 5n2 = 0 + 11n2 + -11n2 12 + 23n + 5n2 = 11n2 + -11n2 Combine like terms: 11n2 + -11n2 = 0 12 + 23n + 5n2 = 0 Factor a trinomial. (4 + n)(3 + 5n) = 0Subproblem 1
Set the factor '(4 + n)' equal to zero and attempt to solve: Simplifying 4 + n = 0 Solving 4 + n = 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 + n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + n = 0 + -4 n = 0 + -4 Combine like terms: 0 + -4 = -4 n = -4 Simplifying n = -4Subproblem 2
Set the factor '(3 + 5n)' equal to zero and attempt to solve: Simplifying 3 + 5n = 0 Solving 3 + 5n = 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 + 5n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5n = 0 + -3 5n = 0 + -3 Combine like terms: 0 + -3 = -3 5n = -3 Divide each side by '5'. n = -0.6 Simplifying n = -0.6Solution
n = {-4, -0.6}
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