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Simplifying (2n + 3)(2n + 1) = 0 Reorder the terms: (3 + 2n)(2n + 1) = 0 Reorder the terms: (3 + 2n)(1 + 2n) = 0 Multiply (3 + 2n) * (1 + 2n) (3(1 + 2n) + 2n * (1 + 2n)) = 0 ((1 * 3 + 2n * 3) + 2n * (1 + 2n)) = 0 ((3 + 6n) + 2n * (1 + 2n)) = 0 (3 + 6n + (1 * 2n + 2n * 2n)) = 0 (3 + 6n + (2n + 4n2)) = 0 Combine like terms: 6n + 2n = 8n (3 + 8n + 4n2) = 0 Solving 3 + 8n + 4n2 = 0 Solving for variable 'n'. Factor a trinomial. (3 + 2n)(1 + 2n) = 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 '(1 + 2n)' equal to zero and attempt to solve: Simplifying 1 + 2n = 0 Solving 1 + 2n = 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 + 2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2n = 0 + -1 2n = 0 + -1 Combine like terms: 0 + -1 = -1 2n = -1 Divide each side by '2'. n = -0.5 Simplifying n = -0.5Solution
n = {-1.5, -0.5}
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