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Simplifying 0 = (7n + 1)(8n + 3) Reorder the terms: 0 = (1 + 7n)(8n + 3) Reorder the terms: 0 = (1 + 7n)(3 + 8n) Multiply (1 + 7n) * (3 + 8n) 0 = (1(3 + 8n) + 7n * (3 + 8n)) 0 = ((3 * 1 + 8n * 1) + 7n * (3 + 8n)) 0 = ((3 + 8n) + 7n * (3 + 8n)) 0 = (3 + 8n + (3 * 7n + 8n * 7n)) 0 = (3 + 8n + (21n + 56n2)) Combine like terms: 8n + 21n = 29n 0 = (3 + 29n + 56n2) Solving 0 = 3 + 29n + 56n2 Solving for variable 'n'. Combine like terms: 0 + -3 = -3 -3 + -29n + -56n2 = 3 + 29n + 56n2 + -3 + -29n + -56n2 Reorder the terms: -3 + -29n + -56n2 = 3 + -3 + 29n + -29n + 56n2 + -56n2 Combine like terms: 3 + -3 = 0 -3 + -29n + -56n2 = 0 + 29n + -29n + 56n2 + -56n2 -3 + -29n + -56n2 = 29n + -29n + 56n2 + -56n2 Combine like terms: 29n + -29n = 0 -3 + -29n + -56n2 = 0 + 56n2 + -56n2 -3 + -29n + -56n2 = 56n2 + -56n2 Combine like terms: 56n2 + -56n2 = 0 -3 + -29n + -56n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 29n + 56n2) = 0 Factor a trinomial. -1((3 + 8n)(1 + 7n)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 8n)' equal to zero and attempt to solve: Simplifying 3 + 8n = 0 Solving 3 + 8n = 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 + 8n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8n = 0 + -3 8n = 0 + -3 Combine like terms: 0 + -3 = -3 8n = -3 Divide each side by '8'. n = -0.375 Simplifying n = -0.375Subproblem 2
Set the factor '(1 + 7n)' equal to zero and attempt to solve: Simplifying 1 + 7n = 0 Solving 1 + 7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 7n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 7n = 0 + -1 7n = 0 + -1 Combine like terms: 0 + -1 = -1 7n = -1 Divide each side by '7'. n = -0.1428571429 Simplifying n = -0.1428571429Solution
n = {-0.375, -0.1428571429}
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