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Simplifying (6n + 1)(n + 8) = 0 Reorder the terms: (1 + 6n)(n + 8) = 0 Reorder the terms: (1 + 6n)(8 + n) = 0 Multiply (1 + 6n) * (8 + n) (1(8 + n) + 6n * (8 + n)) = 0 ((8 * 1 + n * 1) + 6n * (8 + n)) = 0 ((8 + 1n) + 6n * (8 + n)) = 0 (8 + 1n + (8 * 6n + n * 6n)) = 0 (8 + 1n + (48n + 6n2)) = 0 Combine like terms: 1n + 48n = 49n (8 + 49n + 6n2) = 0 Solving 8 + 49n + 6n2 = 0 Solving for variable 'n'. Factor a trinomial. (8 + n)(1 + 6n) = 0Subproblem 1
Set the factor '(8 + n)' equal to zero and attempt to solve: Simplifying 8 + n = 0 Solving 8 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + n = 0 + -8 n = 0 + -8 Combine like terms: 0 + -8 = -8 n = -8 Simplifying n = -8Subproblem 2
Set the factor '(1 + 6n)' equal to zero and attempt to solve: Simplifying 1 + 6n = 0 Solving 1 + 6n = 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 + 6n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6n = 0 + -1 6n = 0 + -1 Combine like terms: 0 + -1 = -1 6n = -1 Divide each side by '6'. n = -0.1666666667 Simplifying n = -0.1666666667Solution
n = {-8, -0.1666666667}
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