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Simplifying (3n + 10)(n + 2) = 0 Reorder the terms: (10 + 3n)(n + 2) = 0 Reorder the terms: (10 + 3n)(2 + n) = 0 Multiply (10 + 3n) * (2 + n) (10(2 + n) + 3n * (2 + n)) = 0 ((2 * 10 + n * 10) + 3n * (2 + n)) = 0 ((20 + 10n) + 3n * (2 + n)) = 0 (20 + 10n + (2 * 3n + n * 3n)) = 0 (20 + 10n + (6n + 3n2)) = 0 Combine like terms: 10n + 6n = 16n (20 + 16n + 3n2) = 0 Solving 20 + 16n + 3n2 = 0 Solving for variable 'n'. Factor a trinomial. (10 + 3n)(2 + n) = 0Subproblem 1
Set the factor '(10 + 3n)' equal to zero and attempt to solve: Simplifying 10 + 3n = 0 Solving 10 + 3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 3n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 3n = 0 + -10 3n = 0 + -10 Combine like terms: 0 + -10 = -10 3n = -10 Divide each side by '3'. n = -3.333333333 Simplifying n = -3.333333333Subproblem 2
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 = -2Solution
n = {-3.333333333, -2}
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