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Simplifying (3n + 4)(2n + 3) = 0 Reorder the terms: (4 + 3n)(2n + 3) = 0 Reorder the terms: (4 + 3n)(3 + 2n) = 0 Multiply (4 + 3n) * (3 + 2n) (4(3 + 2n) + 3n * (3 + 2n)) = 0 ((3 * 4 + 2n * 4) + 3n * (3 + 2n)) = 0 ((12 + 8n) + 3n * (3 + 2n)) = 0 (12 + 8n + (3 * 3n + 2n * 3n)) = 0 (12 + 8n + (9n + 6n2)) = 0 Combine like terms: 8n + 9n = 17n (12 + 17n + 6n2) = 0 Solving 12 + 17n + 6n2 = 0 Solving for variable 'n'. Factor a trinomial. (3 + 2n)(4 + 3n) = 0Subproblem 1
Set the factor '(3 + 2n)' equal to zero and attempt to solve: Simplifying 3 + 2n = 0 Solving 3 + 2n = 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 + 2n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2n = 0 + -3 2n = 0 + -3 Combine like terms: 0 + -3 = -3 2n = -3 Divide each side by '2'. n = -1.5 Simplifying n = -1.5Subproblem 2
Set the factor '(4 + 3n)' equal to zero and attempt to solve: Simplifying 4 + 3n = 0 Solving 4 + 3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3n = 0 + -4 3n = 0 + -4 Combine like terms: 0 + -4 = -4 3n = -4 Divide each side by '3'. n = -1.333333333 Simplifying n = -1.333333333Solution
n = {-1.5, -1.333333333}
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