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Simplifying 6n(n + -2) + 4n(1 + -7n) = 0 Reorder the terms: 6n(-2 + n) + 4n(1 + -7n) = 0 (-2 * 6n + n * 6n) + 4n(1 + -7n) = 0 (-12n + 6n2) + 4n(1 + -7n) = 0 -12n + 6n2 + (1 * 4n + -7n * 4n) = 0 -12n + 6n2 + (4n + -28n2) = 0 Reorder the terms: -12n + 4n + 6n2 + -28n2 = 0 Combine like terms: -12n + 4n = -8n -8n + 6n2 + -28n2 = 0 Combine like terms: 6n2 + -28n2 = -22n2 -8n + -22n2 = 0 Solving -8n + -22n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '-2n'. -2n(4 + 11n) = 0 Ignore the factor -2.Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(4 + 11n)' equal to zero and attempt to solve: Simplifying 4 + 11n = 0 Solving 4 + 11n = 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 + 11n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 11n = 0 + -4 11n = 0 + -4 Combine like terms: 0 + -4 = -4 11n = -4 Divide each side by '11'. n = -0.3636363636 Simplifying n = -0.3636363636Solution
n = {0, -0.3636363636}
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