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Simplifying 8n(8n + 2) + n(6n + 9) = 0 Reorder the terms: 8n(2 + 8n) + n(6n + 9) = 0 (2 * 8n + 8n * 8n) + n(6n + 9) = 0 (16n + 64n2) + n(6n + 9) = 0 Reorder the terms: 16n + 64n2 + n(9 + 6n) = 0 16n + 64n2 + (9 * n + 6n * n) = 0 16n + 64n2 + (9n + 6n2) = 0 Reorder the terms: 16n + 9n + 64n2 + 6n2 = 0 Combine like terms: 16n + 9n = 25n 25n + 64n2 + 6n2 = 0 Combine like terms: 64n2 + 6n2 = 70n2 25n + 70n2 = 0 Solving 25n + 70n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '5n'. 5n(5 + 14n) = 0 Ignore the factor 5.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 '(5 + 14n)' equal to zero and attempt to solve: Simplifying 5 + 14n = 0 Solving 5 + 14n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 14n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 14n = 0 + -5 14n = 0 + -5 Combine like terms: 0 + -5 = -5 14n = -5 Divide each side by '14'. n = -0.3571428571 Simplifying n = -0.3571428571Solution
n = {0, -0.3571428571}
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