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Simplifying (3n + 5)(n + 3) = 0 Reorder the terms: (5 + 3n)(n + 3) = 0 Reorder the terms: (5 + 3n)(3 + n) = 0 Multiply (5 + 3n) * (3 + n) (5(3 + n) + 3n * (3 + n)) = 0 ((3 * 5 + n * 5) + 3n * (3 + n)) = 0 ((15 + 5n) + 3n * (3 + n)) = 0 (15 + 5n + (3 * 3n + n * 3n)) = 0 (15 + 5n + (9n + 3n2)) = 0 Combine like terms: 5n + 9n = 14n (15 + 14n + 3n2) = 0 Solving 15 + 14n + 3n2 = 0 Solving for variable 'n'. Factor a trinomial. (3 + n)(5 + 3n) = 0Subproblem 1
Set the factor '(3 + n)' equal to zero and attempt to solve: Simplifying 3 + n = 0 Solving 3 + n = 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 + n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + n = 0 + -3 n = 0 + -3 Combine like terms: 0 + -3 = -3 n = -3 Simplifying n = -3Subproblem 2
Set the factor '(5 + 3n)' equal to zero and attempt to solve: Simplifying 5 + 3n = 0 Solving 5 + 3n = 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 + 3n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3n = 0 + -5 3n = 0 + -5 Combine like terms: 0 + -5 = -5 3n = -5 Divide each side by '3'. n = -1.666666667 Simplifying n = -1.666666667Solution
n = {-3, -1.666666667}
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