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Simplifying (n + 1)(n + 1) + n(n + 1)(2n + 1) = 0 Reorder the terms: (1 + n)(n + 1) + n(n + 1)(2n + 1) = 0 Reorder the terms: (1 + n)(1 + n) + n(n + 1)(2n + 1) = 0 Multiply (1 + n) * (1 + n) (1(1 + n) + n(1 + n)) + n(n + 1)(2n + 1) = 0 ((1 * 1 + n * 1) + n(1 + n)) + n(n + 1)(2n + 1) = 0 ((1 + 1n) + n(1 + n)) + n(n + 1)(2n + 1) = 0 (1 + 1n + (1 * n + n * n)) + n(n + 1)(2n + 1) = 0 (1 + 1n + (1n + n2)) + n(n + 1)(2n + 1) = 0 Combine like terms: 1n + 1n = 2n (1 + 2n + n2) + n(n + 1)(2n + 1) = 0 Reorder the terms: 1 + 2n + n2 + n(1 + n)(2n + 1) = 0 Reorder the terms: 1 + 2n + n2 + n(1 + n)(1 + 2n) = 0 Multiply (1 + n) * (1 + 2n) 1 + 2n + n2 + n(1(1 + 2n) + n(1 + 2n)) = 0 1 + 2n + n2 + n((1 * 1 + 2n * 1) + n(1 + 2n)) = 0 1 + 2n + n2 + n((1 + 2n) + n(1 + 2n)) = 0 1 + 2n + n2 + n(1 + 2n + (1 * n + 2n * n)) = 0 1 + 2n + n2 + n(1 + 2n + (1n + 2n2)) = 0 Combine like terms: 2n + 1n = 3n 1 + 2n + n2 + n(1 + 3n + 2n2) = 0 1 + 2n + n2 + (1 * n + 3n * n + 2n2 * n) = 0 1 + 2n + n2 + (1n + 3n2 + 2n3) = 0 Reorder the terms: 1 + 2n + 1n + n2 + 3n2 + 2n3 = 0 Combine like terms: 2n + 1n = 3n 1 + 3n + n2 + 3n2 + 2n3 = 0 Combine like terms: n2 + 3n2 = 4n2 1 + 3n + 4n2 + 2n3 = 0 Solving 1 + 3n + 4n2 + 2n3 = 0 Solving for variable 'n'. The solution to this equation could not be determined.
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