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Simplifying (3n + 5)(n + 3) = 7 Reorder the terms: (5 + 3n)(n + 3) = 7 Reorder the terms: (5 + 3n)(3 + n) = 7 Multiply (5 + 3n) * (3 + n) (5(3 + n) + 3n * (3 + n)) = 7 ((3 * 5 + n * 5) + 3n * (3 + n)) = 7 ((15 + 5n) + 3n * (3 + n)) = 7 (15 + 5n + (3 * 3n + n * 3n)) = 7 (15 + 5n + (9n + 3n2)) = 7 Combine like terms: 5n + 9n = 14n (15 + 14n + 3n2) = 7 Solving 15 + 14n + 3n2 = 7 Solving for variable 'n'. Reorder the terms: 15 + -7 + 14n + 3n2 = 7 + -7 Combine like terms: 15 + -7 = 8 8 + 14n + 3n2 = 7 + -7 Combine like terms: 7 + -7 = 0 8 + 14n + 3n2 = 0 Factor a trinomial. (4 + n)(2 + 3n) = 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 '(2 + 3n)' equal to zero and attempt to solve: Simplifying 2 + 3n = 0 Solving 2 + 3n = 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 + 3n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3n = 0 + -2 3n = 0 + -2 Combine like terms: 0 + -2 = -2 3n = -2 Divide each side by '3'. n = -0.6666666667 Simplifying n = -0.6666666667Solution
n = {-4, -0.6666666667}
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