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Simplifying 18n2 + -32n = 11n2 + -9 + -8n Reorder the terms: -32n + 18n2 = 11n2 + -9 + -8n Reorder the terms: -32n + 18n2 = -9 + -8n + 11n2 Solving -32n + 18n2 = -9 + -8n + 11n2 Solving for variable 'n'. Reorder the terms: 9 + -32n + 8n + 18n2 + -11n2 = -9 + -8n + 11n2 + 9 + 8n + -11n2 Combine like terms: -32n + 8n = -24n 9 + -24n + 18n2 + -11n2 = -9 + -8n + 11n2 + 9 + 8n + -11n2 Combine like terms: 18n2 + -11n2 = 7n2 9 + -24n + 7n2 = -9 + -8n + 11n2 + 9 + 8n + -11n2 Reorder the terms: 9 + -24n + 7n2 = -9 + 9 + -8n + 8n + 11n2 + -11n2 Combine like terms: -9 + 9 = 0 9 + -24n + 7n2 = 0 + -8n + 8n + 11n2 + -11n2 9 + -24n + 7n2 = -8n + 8n + 11n2 + -11n2 Combine like terms: -8n + 8n = 0 9 + -24n + 7n2 = 0 + 11n2 + -11n2 9 + -24n + 7n2 = 11n2 + -11n2 Combine like terms: 11n2 + -11n2 = 0 9 + -24n + 7n2 = 0 Factor a trinomial. (3 + -7n)(3 + -1n) = 0Subproblem 1
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 = 0.4285714286Subproblem 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 = {0.4285714286, 3}
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