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Simplifying 5(6n + 1)(n + 2) = 0 Reorder the terms: 5(1 + 6n)(n + 2) = 0 Reorder the terms: 5(1 + 6n)(2 + n) = 0 Multiply (1 + 6n) * (2 + n) 5(1(2 + n) + 6n * (2 + n)) = 0 5((2 * 1 + n * 1) + 6n * (2 + n)) = 0 5((2 + 1n) + 6n * (2 + n)) = 0 5(2 + 1n + (2 * 6n + n * 6n)) = 0 5(2 + 1n + (12n + 6n2)) = 0 Combine like terms: 1n + 12n = 13n 5(2 + 13n + 6n2) = 0 (2 * 5 + 13n * 5 + 6n2 * 5) = 0 (10 + 65n + 30n2) = 0 Solving 10 + 65n + 30n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '5'. 5(2 + 13n + 6n2) = 0 Factor a trinomial. 5((2 + n)(1 + 6n)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2Subproblem 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 = {-2, -0.1666666667}
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