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Simplifying (N)(n + 2)(n + 3)(n + 4) = -66 Reorder the terms: N(2 + n)(n + 3)(n + 4) = -66 Reorder the terms: N(2 + n)(3 + n)(n + 4) = -66 Reorder the terms: N(2 + n)(3 + n)(4 + n) = -66 Multiply (2 + n) * (3 + n) N(2(3 + n) + n(3 + n))(4 + n) = -66 N((3 * 2 + n * 2) + n(3 + n))(4 + n) = -66 N((6 + 2n) + n(3 + n))(4 + n) = -66 N(6 + 2n + (3 * n + n * n))(4 + n) = -66 N(6 + 2n + (3n + n2))(4 + n) = -66 Combine like terms: 2n + 3n = 5n N(6 + 5n + n2)(4 + n) = -66 Multiply (6 + 5n + n2) * (4 + n) N(6(4 + n) + 5n * (4 + n) + n2(4 + n)) = -66 N((4 * 6 + n * 6) + 5n * (4 + n) + n2(4 + n)) = -66 N((24 + 6n) + 5n * (4 + n) + n2(4 + n)) = -66 N(24 + 6n + (4 * 5n + n * 5n) + n2(4 + n)) = -66 N(24 + 6n + (20n + 5n2) + n2(4 + n)) = -66 N(24 + 6n + 20n + 5n2 + (4 * n2 + n * n2)) = -66 N(24 + 6n + 20n + 5n2 + (4n2 + n3)) = -66 Combine like terms: 6n + 20n = 26n N(24 + 26n + 5n2 + 4n2 + n3) = -66 Combine like terms: 5n2 + 4n2 = 9n2 N(24 + 26n + 9n2 + n3) = -66 (24 * N + 26n * N + 9n2 * N + n3 * N) = -66 (24N + 26nN + 9n2N + n3N) = -66 Solving 24N + 26nN + 9n2N + n3N = -66 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Reorder the terms: 66 + 24N + 26nN + 9n2N + n3N = -66 + 66 Combine like terms: -66 + 66 = 0 66 + 24N + 26nN + 9n2N + n3N = 0 The solution to this equation could not be determined.
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