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Simplifying (n + 5)(3n + 2) = 0 Reorder the terms: (5 + n)(3n + 2) = 0 Reorder the terms: (5 + n)(2 + 3n) = 0 Multiply (5 + n) * (2 + 3n) (5(2 + 3n) + n(2 + 3n)) = 0 ((2 * 5 + 3n * 5) + n(2 + 3n)) = 0 ((10 + 15n) + n(2 + 3n)) = 0 (10 + 15n + (2 * n + 3n * n)) = 0 (10 + 15n + (2n + 3n2)) = 0 Combine like terms: 15n + 2n = 17n (10 + 17n + 3n2) = 0 Solving 10 + 17n + 3n2 = 0 Solving for variable 'n'. Factor a trinomial. (5 + n)(2 + 3n) = 0Subproblem 1
Set the factor '(5 + n)' equal to zero and attempt to solve: Simplifying 5 + n = 0 Solving 5 + n = 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 + n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + n = 0 + -5 n = 0 + -5 Combine like terms: 0 + -5 = -5 n = -5 Simplifying n = -5Subproblem 2
Set the factor '(2 + 3n)' equal to zero and attempt to solve: Simplifying 2 + 3n = 0 Solving 2 + 3n = 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 + 3n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3n = 0 + -2 3n = 0 + -2 Combine like terms: 0 + -2 = -2 3n = -2 Divide each side by '3'. n = -0.6666666667 Simplifying n = -0.6666666667Solution
n = {-5, -0.6666666667}
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