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Simplifying (n + 3)(2n + 3) = n2 + 4 + n2 + -4 Reorder the terms: (3 + n)(2n + 3) = n2 + 4 + n2 + -4 Reorder the terms: (3 + n)(3 + 2n) = n2 + 4 + n2 + -4 Multiply (3 + n) * (3 + 2n) (3(3 + 2n) + n(3 + 2n)) = n2 + 4 + n2 + -4 ((3 * 3 + 2n * 3) + n(3 + 2n)) = n2 + 4 + n2 + -4 ((9 + 6n) + n(3 + 2n)) = n2 + 4 + n2 + -4 (9 + 6n + (3 * n + 2n * n)) = n2 + 4 + n2 + -4 (9 + 6n + (3n + 2n2)) = n2 + 4 + n2 + -4 Combine like terms: 6n + 3n = 9n (9 + 9n + 2n2) = n2 + 4 + n2 + -4 Reorder the terms: 9 + 9n + 2n2 = 4 + -4 + n2 + n2 Combine like terms: 4 + -4 = 0 9 + 9n + 2n2 = 0 + n2 + n2 9 + 9n + 2n2 = n2 + n2 Combine like terms: n2 + n2 = 2n2 9 + 9n + 2n2 = 2n2 Add '-2n2' to each side of the equation. 9 + 9n + 2n2 + -2n2 = 2n2 + -2n2 Combine like terms: 2n2 + -2n2 = 0 9 + 9n + 0 = 2n2 + -2n2 9 + 9n = 2n2 + -2n2 Combine like terms: 2n2 + -2n2 = 0 9 + 9n = 0 Solving 9 + 9n = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 9n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 9n = 0 + -9 9n = 0 + -9 Combine like terms: 0 + -9 = -9 9n = -9 Divide each side by '9'. n = -1 Simplifying n = -1
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