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Simplifying (n + 4)(2n + 7) = 0 Reorder the terms: (4 + n)(2n + 7) = 0 Reorder the terms: (4 + n)(7 + 2n) = 0 Multiply (4 + n) * (7 + 2n) (4(7 + 2n) + n(7 + 2n)) = 0 ((7 * 4 + 2n * 4) + n(7 + 2n)) = 0 ((28 + 8n) + n(7 + 2n)) = 0 (28 + 8n + (7 * n + 2n * n)) = 0 (28 + 8n + (7n + 2n2)) = 0 Combine like terms: 8n + 7n = 15n (28 + 15n + 2n2) = 0 Solving 28 + 15n + 2n2 = 0 Solving for variable 'n'. Factor a trinomial. (4 + n)(7 + 2n) = 0Subproblem 1
Set the factor '(4 + n)' equal to zero and attempt to solve: Simplifying 4 + n = 0 Solving 4 + n = 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 + n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + n = 0 + -4 n = 0 + -4 Combine like terms: 0 + -4 = -4 n = -4 Simplifying n = -4Subproblem 2
Set the factor '(7 + 2n)' equal to zero and attempt to solve: Simplifying 7 + 2n = 0 Solving 7 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2n = 0 + -7 2n = 0 + -7 Combine like terms: 0 + -7 = -7 2n = -7 Divide each side by '2'. n = -3.5 Simplifying n = -3.5Solution
n = {-4, -3.5}
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