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Simplifying (10 + n)(9 + n)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(n + -1) = 0 Reorder the terms: (10 + n)(9 + n)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Multiply (10 + n) * (9 + n) (10(9 + n) + n(9 + n))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 ((9 * 10 + n * 10) + n(9 + n))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 ((90 + 10n) + n(9 + n))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (90 + 10n + (9 * n + n * n))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (90 + 10n + (9n + n2))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 10n + 9n = 19n (90 + 19n + n2)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Multiply (90 + 19n + n2) * (8 + n) (90(8 + n) + 19n * (8 + n) + n2(8 + n))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 ((8 * 90 + n * 90) + 19n * (8 + n) + n2(8 + n))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 ((720 + 90n) + 19n * (8 + n) + n2(8 + n))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (720 + 90n + (8 * 19n + n * 19n) + n2(8 + n))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (720 + 90n + (152n + 19n2) + n2(8 + n))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (720 + 90n + 152n + 19n2 + (8 * n2 + n * n2))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (720 + 90n + 152n + 19n2 + (8n2 + n3))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 90n + 152n = 242n (720 + 242n + 19n2 + 8n2 + n3)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 19n2 + 8n2 = 27n2 (720 + 242n + 27n2 + n3)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Multiply (720 + 242n + 27n2 + n3) * (7 + n) (720(7 + n) + 242n * (7 + n) + 27n2 * (7 + n) + n3(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 ((7 * 720 + n * 720) + 242n * (7 + n) + 27n2 * (7 + n) + n3(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 ((5040 + 720n) + 242n * (7 + n) + 27n2 * (7 + n) + n3(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (5040 + 720n + (7 * 242n + n * 242n) + 27n2 * (7 + n) + n3(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (5040 + 720n + (1694n + 242n2) + 27n2 * (7 + n) + n3(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (5040 + 720n + 1694n + 242n2 + (7 * 27n2 + n * 27n2) + n3(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (5040 + 720n + 1694n + 242n2 + (189n2 + 27n3) + n3(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (5040 + 720n + 1694n + 242n2 + 189n2 + 27n3 + (7 * n3 + n * n3))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (5040 + 720n + 1694n + 242n2 + 189n2 + 27n3 + (7n3 + n4))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 720n + 1694n = 2414n (5040 + 2414n + 242n2 + 189n2 + 27n3 + 7n3 + n4)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 242n2 + 189n2 = 431n2 (5040 + 2414n + 431n2 + 27n3 + 7n3 + n4)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 27n3 + 7n3 = 34n3 (5040 + 2414n + 431n2 + 34n3 + n4)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Multiply (5040 + 2414n + 431n2 + 34n3 + n4) * (6 + n) (5040(6 + n) + 2414n * (6 + n) + 431n2 * (6 + n) + 34n3 * (6 + n) + n4(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 ((6 * 5040 + n * 5040) + 2414n * (6 + n) + 431n2 * (6 + n) + 34n3 * (6 + n) + n4(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 ((30240 + 5040n) + 2414n * (6 + n) + 431n2 * (6 + n) + 34n3 * (6 + n) + n4(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (30240 + 5040n + (6 * 2414n + n * 2414n) + 431n2 * (6 + n) + 34n3 * (6 + n) + n4(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (30240 + 5040n + (14484n + 2414n2) + 431n2 * (6 + n) + 34n3 * (6 + n) + n4(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (30240 + 5040n + 14484n + 2414n2 + (6 * 431n2 + n * 431n2) + 34n3 * (6 + n) + n4(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (30240 + 5040n + 14484n + 2414n2 + (2586n2 + 431n3) + 34n3 * (6 + n) + n4(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (30240 + 5040n + 14484n + 2414n2 + 2586n2 + 431n3 + (6 * 34n3 + n * 34n3) + n4(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (30240 + 5040n + 14484n + 2414n2 + 2586n2 + 431n3 + (204n3 + 34n4) + n4(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (30240 + 5040n + 14484n + 2414n2 + 2586n2 + 431n3 + 204n3 + 34n4 + (6 * n4 + n * n4))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (30240 + 5040n + 14484n + 2414n2 + 2586n2 + 431n3 + 204n3 + 34n4 + (6n4 + n5))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 5040n + 14484n = 19524n (30240 + 19524n + 2414n2 + 2586n2 + 431n3 + 204n3 + 34n4 + 6n4 + n5)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 2414n2 + 2586n2 = 5000n2 (30240 + 19524n + 5000n2 + 431n3 + 204n3 + 34n4 + 6n4 + n5)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 431n3 + 204n3 = 635n3 (30240 + 19524n + 5000n2 + 635n3 + 34n4 + 6n4 + n5)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 34n4 + 6n4 = 40n4 (30240 + 19524n + 5000n2 + 635n3 + 40n4 + n5)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Multiply (30240 + 19524n + 5000n2 + 635n3 + 40n4 + n5) * (5 + n) (30240(5 + n) + 19524n * (5 + n) + 5000n2 * (5 + n) + 635n3 * (5 + n) + 40n4 * (5 + n) + n5(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n) = 0 ((5 * 30240 + n * 30240) + 19524n * (5 + n) + 5000n2 * (5 + n) + 635n3 * (5 + n) + 40n4 * (5 + n) + n5(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n) = 0 ((151200 + 30240n) + 19524n * (5 + n) + 5000n2 * (5 + n) + 635n3 * (5 + n) + 40n4 * (5 + n) + n5(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (151200 + 30240n + (5 * 19524n + n * 19524n) + 5000n2 * (5 + n) + 635n3 * (5 + n) + 40n4 * (5 + n) + n5(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (151200 + 30240n + (97620n + 19524n2) + 5000n2 * (5 + n) + 635n3 * (5 + n) + 40n4 * (5 + n) + n5(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (151200 + 30240n + 97620n + 19524n2 + (5 * 5000n2 + n * 5000n2) + 635n3 * (5 + n) + 40n4 * (5 + n) + n5(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (151200 + 30240n + 97620n + 19524n2 + (25000n2 + 5000n3) + 635n3 * (5 + n) + 40n4 * (5 + n) + n5(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (151200 + 30240n + 97620n + 19524n2 + 25000n2 + 5000n3 + (5 * 635n3 + n * 635n3) + 40n4 * (5 + n) + n5(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (151200 + 30240n + 97620n + 19524n2 + 25000n2 + 5000n3 + (3175n3 + 635n4) + 40n4 * (5 + n) + n5(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (151200 + 30240n + 97620n + 19524n2 + 25000n2 + 5000n3 + 3175n3 + 635n4 + (5 * 40n4 + n * 40n4) + n5(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (151200 + 30240n + 97620n + 19524n2 + 25000n2 + 5000n3 + 3175n3 + 635n4 + (200n4 + 40n5) + n5(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (151200 + 30240n + 97620n + 19524n2 + 25000n2 + 5000n3 + 3175n3 + 635n4 + 200n4 + 40n5 + (5 * n5 + n * n5))(4 + n)(3 + n)(2 + n)(-1 + n) = 0 (151200 + 30240n + 97620n + 19524n2 + 25000n2 + 5000n3 + 3175n3 + 635n4 + 200n4 + 40n5 + (5n5 + n6))(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 30240n + 97620n = 127860n (151200 + 127860n + 19524n2 + 25000n2 + 5000n3 + 3175n3 + 635n4 + 200n4 + 40n5 + 5n5 + n6)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 19524n2 + 25000n2 = 44524n2 (151200 + 127860n + 44524n2 + 5000n3 + 3175n3 + 635n4 + 200n4 + 40n5 + 5n5 + n6)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 5000n3 + 3175n3 = 8175n3 (151200 + 127860n + 44524n2 + 8175n3 + 635n4 + 200n4 + 40n5 + 5n5 + n6)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 635n4 + 200n4 = 835n4 (151200 + 127860n + 44524n2 + 8175n3 + 835n4 + 40n5 + 5n5 + n6)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 40n5 + 5n5 = 45n5 (151200 + 127860n + 44524n2 + 8175n3 + 835n4 + 45n5 + n6)(4 + n)(3 + n)(2 + n)(-1 + n) = 0 Multiply (151200 + 127860n + 44524n2 + 8175n3 + 835n4 + 45n5 + n6) * (4 + n) (151200(4 + n) + 127860n * (4 + n) + 44524n2 * (4 + n) + 8175n3 * (4 + n) + 835n4 * (4 + n) + 45n5 * (4 + n) + n6(4 + n))(3 + n)(2 + n)(-1 + n) = 0 ((4 * 151200 + n * 151200) + 127860n * (4 + n) + 44524n2 * (4 + n) + 8175n3 * (4 + n) + 835n4 * (4 + n) + 45n5 * (4 + n) + n6(4 + n))(3 + n)(2 + n)(-1 + n) = 0 ((604800 + 151200n) + 127860n * (4 + n) + 44524n2 * (4 + n) + 8175n3 * (4 + n) + 835n4 * (4 + n) + 45n5 * (4 + n) + n6(4 + n))(3 + n)(2 + n)(-1 + n) = 0 (604800 + 151200n + (4 * 127860n + n * 127860n) + 44524n2 * (4 + n) + 8175n3 * (4 + n) + 835n4 * (4 + n) + 45n5 * (4 + n) + n6(4 + n))(3 + n)(2 + n)(-1 + n) = 0 (604800 + 151200n + (511440n + 127860n2) + 44524n2 * (4 + n) + 8175n3 * (4 + n) + 835n4 * (4 + n) + 45n5 * (4 + n) + n6(4 + n))(3 + n)(2 + n)(-1 + n) = 0 (604800 + 151200n + 511440n + 127860n2 + (4 * 44524n2 + n * 44524n2) + 8175n3 * (4 + n) + 835n4 * (4 + n) + 45n5 * (4 + n) + n6(4 + n))(3 + n)(2 + n)(-1 + n) = 0 (604800 + 151200n + 511440n + 127860n2 + (178096n2 + 44524n3) + 8175n3 * (4 + n) + 835n4 * (4 + n) + 45n5 * (4 + n) + n6(4 + n))(3 + n)(2 + n)(-1 + n) = 0 (604800 + 151200n + 511440n + 127860n2 + 178096n2 + 44524n3 + (4 * 8175n3 + n * 8175n3) + 835n4 * (4 + n) + 45n5 * (4 + n) + n6(4 + n))(3 + n)(2 + n)(-1 + n) = 0 (604800 + 151200n + 511440n + 127860n2 + 178096n2 + 44524n3 + (32700n3 + 8175n4) + 835n4 * (4 + n) + 45n5 * (4 + n) + n6(4 + n))(3 + n)(2 + n)(-1 + n) = 0 (604800 + 151200n + 511440n + 127860n2 + 178096n2 + 44524n3 + 32700n3 + 8175n4 + (4 * 835n4 + n * 835n4) + 45n5 * (4 + n) + n6(4 + n))(3 + n)(2 + n)(-1 + n) = 0 (604800 + 151200n + 511440n + 127860n2 + 178096n2 + 44524n3 + 32700n3 + 8175n4 + (3340n4 + 835n5) + 45n5 * (4 + n) + n6(4 + n))(3 + n)(2 + n)(-1 + n) = 0 (604800 + 151200n + 511440n + 127860n2 + 178096n2 + 44524n3 + 32700n3 + 8175n4 + 3340n4 + 835n5 + (4 * 45n5 + n * 45n5) + n6(4 + n))(3 + n)(2 + n)(-1 + n) = 0 (604800 + 151200n + 511440n + 127860n2 + 178096n2 + 44524n3 + 32700n3 + 8175n4 + 3340n4 + 835n5 + (180n5 + 45n6) + n6(4 + n))(3 + n)(2 + n)(-1 + n) = 0 (604800 + 151200n + 511440n + 127860n2 + 178096n2 + 44524n3 + 32700n3 + 8175n4 + 3340n4 + 835n5 + 180n5 + 45n6 + (4 * n6 + n * n6))(3 + n)(2 + n)(-1 + n) = 0 (604800 + 151200n + 511440n + 127860n2 + 178096n2 + 44524n3 + 32700n3 + 8175n4 + 3340n4 + 835n5 + 180n5 + 45n6 + (4n6 + n7))(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 151200n + 511440n = 662640n (604800 + 662640n + 127860n2 + 178096n2 + 44524n3 + 32700n3 + 8175n4 + 3340n4 + 835n5 + 180n5 + 45n6 + 4n6 + n7)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 127860n2 + 178096n2 = 305956n2 (604800 + 662640n + 305956n2 + 44524n3 + 32700n3 + 8175n4 + 3340n4 + 835n5 + 180n5 + 45n6 + 4n6 + n7)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 44524n3 + 32700n3 = 77224n3 (604800 + 662640n + 305956n2 + 77224n3 + 8175n4 + 3340n4 + 835n5 + 180n5 + 45n6 + 4n6 + n7)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 8175n4 + 3340n4 = 11515n4 (604800 + 662640n + 305956n2 + 77224n3 + 11515n4 + 835n5 + 180n5 + 45n6 + 4n6 + n7)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 835n5 + 180n5 = 1015n5 (604800 + 662640n + 305956n2 + 77224n3 + 11515n4 + 1015n5 + 45n6 + 4n6 + n7)(3 + n)(2 + n)(-1 + n) = 0 Combine like terms: 45n6 + 4n6 = 49n6 (604800 + 662640n + 305956n2 + 77224n3 + 11515n4 + 1015n5 + 49n6 + n7)(3 + n)(2 + n)(-1 + n) = 0 Multiply (604800 + 662640n + 305956n2 + 77224n3 + 11515n4 + 1015n5 + 49n6 + n7) * (3 + n) (604800(3 + n) + 662640n * (3 + n) + 305956n2 * (3 + n) + 77224n3 * (3 + n) + 11515n4 * (3 + n) + 1015n5 * (3 + n) + 49n6 * (3 + n) + n7(3 + n))(2 + n)(-1 + n) = 0 ((3 * 604800 + n * 604800) + 662640n * (3 + n) + 305956n2 * (3 + n) + 77224n3 * (3 + n) + 11515n4 * (3 + n) + 1015n5 * (3 + n) + 49n6 * (3 + n) + n7(3 + n))(2 + n)(-1 + n) = 0 ((1814400 + 604800n) + 662640n * (3 + n) + 305956n2 * (3 + n) + 77224n3 * (3 + n) + 11515n4 * (3 + n) + 1015n5 * (3 + n) + 49n6 * (3 + n) + n7(3 + n))(2 + n)(-1 + n) = 0 (1814400 + 604800n + (3 * 662640n + n * 662640n) + 305956n2 * (3 + n) + 77224n3 * (3 + n) + 11515n4 * (3 + n) + 1015n5 * (3 + n) + 49n6 * (3 + n) + n7(3 + n))(2 + n)(-1 + n) = 0 (1814400 + 604800n + (1987920n + 662640n2) + 305956n2 * (3 + n) + 77224n3 * (3 + n) + 11515n4 * (3 + n) + 1015n5 * (3 + n) + 49n6 * (3 + n) + n7(3 + n))(2 + n)(-1 + n) = 0 (1814400 + 604800n + 1987920n + 662640n2 + (3 * 305956n2 + n * 305956n2) + 77224n3 * (3 + n) + 11515n4 * (3 + n) + 1015n5 * (3 + n) + 49n6 * (3 + n) + n7(3 + n))(2 + n)(-1 + n) = 0 (1814400 + 604800n + 1987920n + 662640n2 + (917868n2 + 305956n3) + 77224n3 * (3 + n) + 11515n4 * (3 + n) + 1015n5 * (3 + n) + 49n6 * (3 + n) + n7(3 + n))(2 + n)(-1 + n) = 0 (1814400 + 604800n + 1987920n + 662640n2 + 917868n2 + 305956n3 + (3 * 77224n3 + n * 77224n3) + 11515n4 * (3 + n) + 1015n5 * (3 + n) + 49n6 * (3 + n) + n7(3 + n))(2 + n)(-1 + n) = 0 (1814400 + 604800n + 1987920n + 662640n2 + 917868n2 + 305956n3 + (231672n3 + 77224n4) + 11515n4 * (3 + n) + 1015n5 * (3 + n) + 49n6 * (3 + n) + n7(3 + n))(2 + n)(-1 + n) = 0 (1814400 + 604800n + 1987920n + 662640n2 + 917868n2 + 305956n3 + 231672n3 + 77224n4 + (3 * 11515n4 + n * 11515n4) + 1015n5 * (3 + n) + 49n6 * (3 + n) + n7(3 + n))(2 + n)(-1 + n) = 0 (1814400 + 604800n + 1987920n + 662640n2 + 917868n2 + 305956n3 + 231672n3 + 77224n4 + (34545n4 + 11515n5) + 1015n5 * (3 + n) + 49n6 * (3 + n) + n7(3 + n))(2 + n)(-1 + n) = 0 (1814400 + 604800n + 1987920n + 662640n2 + 917868n2 + 305956n3 + 231672n3 + 77224n4 + 34545n4 + 11515n5 + (3 * 1015n5 + n * 1015n5) + 49n6 * (3 + n) + n7(3 + n))(2 + n)(-1 + n) = 0 (1814400 + 604800n + 1987920n + 662640n2 + 917868n2 + 305956n3 + 231672n3 + 77224n4 + 34545n4 + 11515n5 + (3045n5 + 1015n6) + 49n6 * (3 + n) + n7(3 + n))(2 + n)(-1 + n) = 0 (1814400 + 604800n + 1987920n + 662640n2 + 917868n2 + 305956n3 + 231672n3 + 77224n4 + 34545n4 + 11515n5 + 3045n5 + 1015n6 + (3 * 49n6 + n * 49n6) + n7(3 + n))(2 + n)(-1 + n) = 0 (1814400 + 604800n + 1987920n + 662640n2 + 917868n2 + 305956n3 + 231672n3 + 77224n4 + 34545n4 + 11515n5 + 3045n5 + 1015n6 + (147n6 + 49n7) + n7(3 + n))(2 + n)(-1 + n) = 0 (1814400 + 604800n + 1987920n + 662640n2 + 917868n2 + 305956n3 + 231672n3 + 77224n4 + 34545n4 + 11515n5 + 3045n5 + 1015n6 + 147n6 + 49n7 + (3 * n7 + n * n7))(2 + n)(-1 + n) = 0 (1814400 + 604800n + 1987920n + 662640n2 + 917868n2 + 305956n3 + 231672n3 + 77224n4 + 34545n4 + 11515n5 + 3045n5 + 1015n6 + 147n6 + 49n7 + (3n7 + n8))(2 + n)(-1 + n) = 0 Combine like terms: 604800n + 1987920n = 2592720n (1814400 + 2592720n + 662640n2 + 917868n2 + 305956n3 + 231672n3 + 77224n4 + 34545n4 + 11515n5 + 3045n5 + 1015n6 + 147n6 + 49n7 + 3n7 + n8)(2 + n)(-1 + n) = 0 Combine like terms: 662640n2 + 917868n2 = 1580508n2 (1814400 + 2592720n + 1580508n2 + 305956n3 + 231672n3 + 77224n4 + 34545n4 + 11515n5 + 3045n5 + 1015n6 + 147n6 + 49n7 + 3n7 + n8)(2 + n)(-1 + n) = 0 Combine like terms: 305956n3 + 231672n3 = 537628n3 (1814400 + 2592720n + 1580508n2 + 537628n3 + 77224n4 + 34545n4 + 11515n5 + 3045n5 + 1015n6 + 147n6 + 49n7 + 3n7 + n8)(2 + n)(-1 + n) = 0 Combine like terms: 77224n4 + 34545n4 = 111769n4 (1814400 + 2592720n + 1580508n2 + 537628n3 + 111769n4 + 11515n5 + 3045n5 + 1015n6 + 147n6 + 49n7 + 3n7 + n8)(2 + n)(-1 + n) = 0 Combine like terms: 11515n5 + 3045n5 = 14560n5 (1814400 + 2592720n + 1580508n2 + 537628n3 + 111769n4 + 14560n5 + 1015n6 + 147n6 + 49n7 + 3n7 + n8)(2 + n)(-1 + n) = 0 Combine like terms: 1015n6 + 147n6 = 1162n6 (1814400 + 2592720n + 1580508n2 + 537628n3 + 111769n4 + 14560n5 + 1162n6 + 49n7 + 3n7 + n8)(2 + n)(-1 + n) = 0 Combine like terms: 49n7 + 3n7 = 52n7 (1814400 + 2592720n + 1580508n2 + 537628n3 + 111769n4 + 14560n5 + 1162n6 + 52n7 + n8)(2 + n)(-1 + n) = 0 Multiply (1814400 + 2592720n + 1580508n2 + 537628n3 + 111769n4 + 14560n5 + 1162n6 + 52n7 + n8) * (2 + n) (1814400(2 + n) + 2592720n * (2 + n) + 1580508n2 * (2 + n) + 537628n3 * (2 + n) + 111769n4 * (2 + n) + 14560n5 * (2 + n) + 1162n6 * (2 + n) + 52n7 * (2 + n) + n8(2 + n))(-1 + n) = 0 ((2 * 1814400 + n * 1814400) + 2592720n * (2 + n) + 1580508n2 * (2 + n) + 537628n3 * (2 + n) + 111769n4 * (2 + n) + 14560n5 * (2 + n) + 1162n6 * (2 + n) + 52n7 * (2 + n) + n8(2 + n))(-1 + n) = 0 ((3628800 + 1814400n) + 2592720n * (2 + n) + 1580508n2 * (2 + n) + 537628n3 * (2 + n) + 111769n4 * (2 + n) + 14560n5 * (2 + n) + 1162n6 * (2 + n) + 52n7 * (2 + n) + n8(2 + n))(-1 + n) = 0 (3628800 + 1814400n + (2 * 2592720n + n * 2592720n) + 1580508n2 * (2 + n) + 537628n3 * (2 + n) + 111769n4 * (2 + n) + 14560n5 * (2 + n) + 1162n6 * (2 + n) + 52n7 * (2 + n) + n8(2 + n))(-1 + n) = 0 (3628800 + 1814400n + (5185440n + 2592720n2) + 1580508n2 * (2 + n) + 537628n3 * (2 + n) + 111769n4 * (2 + n) + 14560n5 * (2 + n) + 1162n6 * (2 + n) + 52n7 * (2 + n) + n8(2 + n))(-1 + n) = 0 (3628800 + 1814400n + 5185440n + 2592720n2 + (2 * 1580508n2 + n * 1580508n2) + 537628n3 * (2 + n) + 111769n4 * (2 + n) + 14560n5 * (2 + n) + 1162n6 * (2 + n) + 52n7 * (2 + n) + n8(2 + n))(-1 + n) = 0 (3628800 + 1814400n + 5185440n + 2592720n2 + (3161016n2 + 1580508n3) + 537628n3 * (2 + n) + 111769n4 * (2 + n) + 14560n5 * (2 + n) + 1162n6 * (2 + n) + 52n7 * (2 + n) + n8(2 + n))(-1 + n) = 0 (3628800 + 1814400n + 5185440n + 2592720n2 + 3161016n2 + 1580508n3 + (2 * 537628n3 + n * 537628n3) + 111769n4 * (2 + n) + 14560n5 * (2 + n) + 1162n6 * (2 + n) + 52n7 * (2 + n) + n8(2 + n))(-1 + n) = 0 (3628800 + 1814400n + 5185440n + 2592720n2 + 3161016n2 + 1580508n3 + (1075256n3 + 537628n4) + 111769n4 * (2 + n) + 14560n5 * (2 + n) + 1162n6 * (2 + n) + 52n7 * (2 + n) + n8(2 + n))(-1 + n) = 0 (3628800 + 1814400n + 5185440n + 2592720n2 + 3161016n2 + 1580508n3 + 1075256n3 + 537628n4 + (2 * 111769n4 + n * 111769n4) + 14560n5 * (2 + n) + 1162n6 * (2 + n) + 52n7 * (2 + n) + n8(2 + n))(-1 + n) = 0 (3628800 + 1814400n + 5185440n + 2592720n2 + 3161016n2 + 1580508n3 + 1075256n3 + 537628n4 + (223538n4 + 111769n5) + 14560n5 * (2 + n) + 1162n6 * (2 + n) + 52n7 * (2 + n) + n8(2 + n))(-1 + n) = 0 (3628800 + 1814400n + 5185440n + 2592720n2 + 3161016n2 + 1580508n3 + 1075256n3 + 537628n4 + 223538n4 + 111769n5 + (2 * 14560n5 + n * 14560n5) + 1162n6 * (2 + n) + 52n7 * (2 + n) + n8(2 + n))(-1 + n) = 0 (3628800 + 1814400n + 5185440n + 2592720n2 + 3161016n2 + 1580508n3 + 1075256n3 + 537628n4 + 223538n4 + 111769n5 + (29120n5 + 14560n6) + 1162n6 * (2 + n) + 52n7 * (2 + n) + n8(2 + n))(-1 + n) = 0 (3628800 + 1814400n + 5185440n + 2592720n2 + 3161016n2 + 1580508n3 + 1075256n3 + 537628n4 + 223538n4 + 111769n5 + 29120n5 + 14560n6 + (2 * 1162n6 + n * 1162n6) + 52n7 * (2 + n) + n8(2 + n))(-1 + n) = 0 (3628800 + 1814400n + 5185440n + 2592720n2 + 3161016n2 + 1580508n3 + 1075256n3 + 537628n4 + 223538n4 + 111769n5 + 29120n5 + 14560n6 + (2324n6 + 1162n7) + 52n7 * (2 + n) + n8(2 + n))(-1 + n) = 0 (3628800 + 1814400n + 5185440n + 2592720n2 + 3161016n2 + 1580508n3 + 1075256n3 + 537628n4 + 223538n4 + 111769n5 + 29120n5 + 14560n6 + 2324n6 + 1162n7 + (2 * 52n7 + n * 52n7) + n8(2 + n))(-1 + n) = 0 (3628800 + 1814400n + 5185440n + 2592720n2 + 3161016n2 + 1580508n3 + 1075256n3 + 537628n4 + 223538n4 + 111769n5 + 29120n5 + 14560n6 + 2324n6 + 1162n7 + (104n7 + 52n8) + n8(2 + n))(-1 + n) = 0 (3628800 + 1814400n + 5185440n + 2592720n2 + 3161016n2 + 1580508n3 + 1075256n3 + 537628n4 + 223538n4 + 111769n5 + 29120n5 + 14560n6 + 2324n6 + 1162n7 + 104n7 + 52n8 + (2 * n8 + n * n8))(-1 + n) = 0 (3628800 + 1814400n + 5185440n + 2592720n2 + 3161016n2 + 1580508n3 + 1075256n3 + 537628n4 + 223538n4 + 111769n5 + 29120n5 + 14560n6 + 2324n6 + 1162n7 + 104n7 + 52n8 + (2n8 + n9))(-1 + n) = 0 Combine like terms: 1814400n + 5185440n = 6999840n (3628800 + 6999840n + 2592720n2 + 3161016n2 + 1580508n3 + 1075256n3 + 537628n4 + 223538n4 + 111769n5 + 29120n5 + 14560n6 + 2324n6 + 1162n7 + 104n7 + 52n8 + 2n8 + n9)(-1 + n) = 0 Combine like terms: 2592720n2 + 3161016n2 = 5753736n2 (3628800 + 6999840n + 5753736n2 + 1580508n3 + 1075256n3 + 537628n4 + 223538n4 + 111769n5 + 29120n5 + 14560n6 + 2324n6 + 1162n7 + 104n7 + 52n8 + 2n8 + n9)(-1 + n) = 0 Combine like terms: 1580508n3 + 1075256n3 = 2655764n3 (3628800 + 6999840n + 5753736n2 + 2655764n3 + 537628n4 + 223538n4 + 111769n5 + 29120n5 + 14560n6 + 2324n6 + 1162n7 + 104n7 + 52n8 + 2n8 + n9)(-1 + n) = 0 Combine like terms: 537628n4 + 223538n4 = 761166n4 (3628800 + 6999840n + 5753736n2 + 2655764n3 + 761166n4 + 111769n5 + 29120n5 + 14560n6 + 2324n6 + 1162n7 + 104n7 + 52n8 + 2n8 + n9)(-1 + n) = 0 Combine like terms: 111769n5 + 29120n5 = 140889n5 (3628800 + 6999840n + 5753736n2 + 2655764n3 + 761166n4 + 140889n5 + 14560n6 + 2324n6 + 1162n7 + 104n7 + 52n8 + 2n8 + n9)(-1 + n) = 0 Combine like terms: 14560n6 + 2324n6 = 16884n6 (3628800 + 6999840n + 5753736n2 + 2655764n3 + 761166n4 + 140889n5 + 16884n6 + 1162n7 + 104n7 + 52n8 + 2n8 + n9)(-1 + n) = 0 Combine like terms: 1162n7 + 104n7 = 1266n7 (3628800 + 6999840n + 5753736n2 + 2655764n3 + 761166n4 + 140889n5 + 16884n6 + 1266n7 + 52n8 + 2n8 + n9)(-1 + n) = 0 Combine like terms: 52n8 + 2n8 = 54n8 (3628800 + 6999840n + 5753736n2 + 2655764n3 + 761166n4 + 140889n5 + 16884n6 + 1266n7 + 54n8 + n9)(-1 + n) = 0 Multiply (3628800 + 6999840n + 5753736n2 + 2655764n3 + 761166n4 + 140889n5 + 16884n6 + 1266n7 + 54n8 + n9) * (-1 + n) (3628800(-1 + n) + 6999840n * (-1 + n) + 5753736n2 * (-1 + n) + 2655764n3 * (-1 + n) + 761166n4 * (-1 + n) + 140889n5 * (-1 + n) + 16884n6 * (-1 + n) + 1266n7 * (-1 + n) + 54n8 * (-1 + n) + n9(-1 + n)) = 0 ((-1 * 3628800 + n * 3628800) + 6999840n * (-1 + n) + 5753736n2 * (-1 + n) + 2655764n3 * (-1 + n) + 761166n4 * (-1 + n) + 140889n5 * (-1 + n) + 16884n6 * (-1 + n) + 1266n7 * (-1 + n) + 54n8 * (-1 + n) + n9(-1 + n)) = 0 ((-3628800 + 3628800n) + 6999840n * (-1 + n) + 5753736n2 * (-1 + n) + 2655764n3 * (-1 + n) + 761166n4 * (-1 + n) + 140889n5 * (-1 + n) + 16884n6 * (-1 + n) + 1266n7 * (-1 + n) + 54n8 * (-1 + n) + n9(-1 + n)) = 0 (-3628800 + 3628800n + (-1 * 6999840n + n * 6999840n) + 5753736n2 * (-1 + n) + 2655764n3 * (-1 + n) + 761166n4 * (-1 + n) + 140889n5 * (-1 + n) + 16884n6 * (-1 + n) + 1266n7 * (-1 + n) + 54n8 * (-1 + n) + n9(-1 + n)) = 0 (-3628800 + 3628800n + (-6999840n + 6999840n2) + 5753736n2 * (-1 + n) + 2655764n3 * (-1 + n) + 761166n4 * (-1 + n) + 140889n5 * (-1 + n) + 16884n6 * (-1 + n) + 1266n7 * (-1 + n) + 54n8 * (-1 + n) + n9(-1 + n)) = 0 (-3628800 + 3628800n + -6999840n + 6999840n2 + (-1 * 5753736n2 + n * 5753736n2) + 2655764n3 * (-1 + n) + 761166n4 * (-1 + n) + 140889n5 * (-1 + n) + 16884n6 * (-1 + n) + 1266n7 * (-1 + n) + 54n8 * (-1 + n) + n9(-1 + n)) = 0 (-3628800 + 3628800n + -6999840n + 6999840n2 + (-5753736n2 + 5753736n3) + 2655764n3 * (-1 + n) + 761166n4 * (-1 + n) + 140889n5 * (-1 + n) + 16884n6 * (-1 + n) + 1266n7 * (-1 + n) + 54n8 * (-1 + n) + n9(-1 + n)) = 0 (-3628800 + 3628800n + -6999840n + 6999840n2 + -5753736n2 + 5753736n3 + (-1 * 2655764n3 + n * 2655764n3) + 761166n4 * (-1 + n) + 140889n5 * (-1 + n) + 16884n6 * (-1 + n) + 1266n7 * (-1 + n) + 54n8 * (-1 + n) + n9(-1 + n)) = 0 (-3628800 + 3628800n + -6999840n + 6999840n2 + -5753736n2 + 5753736n3 + (-2655764n3 + 2655764n4) + 761166n4 * (-1 + n) + 140889n5 * (-1 + n) + 16884n6 * (-1 + n) + 1266n7 * (-1 + n) + 54n8 * (-1 + n) + n9(-1 + n)) = 0 (-3628800 + 3628800n + -6999840n + 6999840n2 + -5753736n2 + 5753736n3 + -2655764n3 + 2655764n4 + (-1 * 761166n4 + n * 761166n4) + 140889n5 * (-1 + n) + 16884n6 * (-1 + n) + 1266n7 * (-1 + n) + 54n8 * (-1 + n) + n9(-1 + n)) = 0 (-3628800 + 3628800n + -6999840n + 6999840n2 + -5753736n2 + 5753736n3 + -2655764n3 + 2655764n4 + (-761166n4 + 761166n5) + 140889n5 * (-1 + n) + 16884n6 * (-1 + n) + 1266n7 * (-1 + n) + 54n8 * (-1 + n) + n9(-1 + n)) = 0 (-3628800 + 3628800n + -6999840n + 6999840n2 + -5753736n2 + 5753736n3 + -2655764n3 + 2655764n4 + -761166n4 + 761166n5 + (-1 * 140889n5 + n * 140889n5) + 16884n6 * (-1 + n) + 1266n7 * (-1 + n) + 54n8 * (-1 + n) + n9(-1 + n)) = 0 (-3628800 + 3628800n + -6999840n + 6999840n2 + -5753736n2 + 5753736n3 + -2655764n3 + 2655764n4 + -761166n4 + 761166n5 + (-140889n5 + 140889n6) + 16884n6 * (-1 + n) + 1266n7 * (-1 + n) + 54n8 * (-1 + n) + n9(-1 + n)) = 0 (-3628800 + 3628800n + -6999840n + 6999840n2 + -5753736n2 + 5753736n3 + -2655764n3 + 2655764n4 + -761166n4 + 761166n5 + -140889n5 + 140889n6 + (-1 * 16884n6 + n * 16884n6) + 1266n7 * (-1 + n) + 54n8 * (-1 + n) + n9(-1 + n)) = 0 (-3628800 + 3628800n + -6999840n + 6999840n2 + -5753736n2 + 5753736n3 + -2655764n3 + 2655764n4 + -761166n4 + 761166n5 + -140889n5 + 140889n6 + (-16884n6 + 16884n7) + 1266n7 * (-1 + n) + 54n8 * (-1 + n) + n9(-1 + n)) = 0 (-3628800 + 3628800n + -6999840n + 6999840n2 + -5753736n2 + 5753736n3 + -2655764n3 + 2655764n4 + -761166n4 + 761166n5 + -140889n5 + 140889n6 + -16884n6 + 16884n7 + (-1 * 1266n7 + n * 1266n7) + 54n8 * (-1 + n) + n9(-1 + n)) = 0 (-3628800 + 3628800n + -6999840n + 6999840n2 + -5753736n2 + 5753736n3 + -2655764n3 + 2655764n4 + -761166n4 + 761166n5 + -140889n5 + 140889n6 + -16884n6 + 16884n7 + (-1266n7 + 1266n8) + 54n8 * (-1 + n) + n9(-1 + n)) = 0 (-3628800 + 3628800n + -6999840n + 6999840n2 + -5753736n2 + 5753736n3 + -2655764n3 + 2655764n4 + -761166n4 + 761166n5 + -140889n5 + 140889n6 + -16884n6 + 16884n7 + -1266n7 + 1266n8 + (-1 * 54n8 + n * 54n8) + n9(-1 + n)) = 0 (-3628800 + 3628800n + -6999840n + 6999840n2 + -5753736n2 + 5753736n3 + -2655764n3 + 2655764n4 + -761166n4 + 761166n5 + -140889n5 + 140889n6 + -16884n6 + 16884n7 + -1266n7 + 1266n8 + (-54n8 + 54n9) + n9(-1 + n)) = 0 (-3628800 + 3628800n + -6999840n + 6999840n2 + -5753736n2 + 5753736n3 + -2655764n3 + 2655764n4 + -761166n4 + 761166n5 + -140889n5 + 140889n6 + -16884n6 + 16884n7 + -1266n7 + 1266n8 + -54n8 + 54n9 + (-1 * n9 + n * n9)) = 0 (-3628800 + 3628800n + -6999840n + 6999840n2 + -5753736n2 + 5753736n3 + -2655764n3 + 2655764n4 + -761166n4 + 761166n5 + -140889n5 + 140889n6 + -16884n6 + 16884n7 + -1266n7 + 1266n8 + -54n8 + 54n9 + (-1n9 + n10)) = 0 Combine like terms: 3628800n + -6999840n = -3371040n (-3628800 + -3371040n + 6999840n2 + -5753736n2 + 5753736n3 + -2655764n3 + 2655764n4 + -761166n4 + 761166n5 + -140889n5 + 140889n6 + -16884n6 + 16884n7 + -1266n7 + 1266n8 + -54n8 + 54n9 + -1n9 + n10) = 0 Combine like terms: 6999840n2 + -5753736n2 = 1246104n2 (-3628800 + -3371040n + 1246104n2 + 5753736n3 + -2655764n3 + 2655764n4 + -761166n4 + 761166n5 + -140889n5 + 140889n6 + -16884n6 + 16884n7 + -1266n7 + 1266n8 + -54n8 + 54n9 + -1n9 + n10) = 0 Combine like terms: 5753736n3 + -2655764n3 = 3097972n3 (-3628800 + -3371040n + 1246104n2 + 3097972n3 + 2655764n4 + -761166n4 + 761166n5 + -140889n5 + 140889n6 + -16884n6 + 16884n7 + -1266n7 + 1266n8 + -54n8 + 54n9 + -1n9 + n10) = 0 Combine like terms: 2655764n4 + -761166n4 = 1894598n4 (-3628800 + -3371040n + 1246104n2 + 3097972n3 + 1894598n4 + 761166n5 + -140889n5 + 140889n6 + -16884n6 + 16884n7 + -1266n7 + 1266n8 + -54n8 + 54n9 + -1n9 + n10) = 0 Combine like terms: 761166n5 + -140889n5 = 620277n5 (-3628800 + -3371040n + 1246104n2 + 3097972n3 + 1894598n4 + 620277n5 + 140889n6 + -16884n6 + 16884n7 + -1266n7 + 1266n8 + -54n8 + 54n9 + -1n9 + n10) = 0 Combine like terms: 140889n6 + -16884n6 = 124005n6 (-3628800 + -3371040n + 1246104n2 + 3097972n3 + 1894598n4 + 620277n5 + 124005n6 + 16884n7 + -1266n7 + 1266n8 + -54n8 + 54n9 + -1n9 + n10) = 0 Combine like terms: 16884n7 + -1266n7 = 15618n7 (-3628800 + -3371040n + 1246104n2 + 3097972n3 + 1894598n4 + 620277n5 + 124005n6 + 15618n7 + 1266n8 + -54n8 + 54n9 + -1n9 + n10) = 0 Combine like terms: 1266n8 + -54n8 = 1212n8 (-3628800 + -3371040n + 1246104n2 + 3097972n3 + 1894598n4 + 620277n5 + 124005n6 + 15618n7 + 1212n8 + 54n9 + -1n9 + n10) = 0 Combine like terms: 54n9 + -1n9 = 53n9 (-3628800 + -3371040n + 1246104n2 + 3097972n3 + 1894598n4 + 620277n5 + 124005n6 + 15618n7 + 1212n8 + 53n9 + n10) = 0 Solving -3628800 + -3371040n + 1246104n2 + 3097972n3 + 1894598n4 + 620277n5 + 124005n6 + 15618n7 + 1212n8 + 53n9 + n10 = 0 Solving for variable 'n'. The solution to this equation could not be determined.
| 4x(3x-2)=2x(3x+14) | | 2x^2+5x=33 | | -112=-3[8-2n]+5n | | 10a^3b+10a^2b=0 | | p^2+2p=3 | | 11(4+-6y)+5(13y+1)=9 | | 3x(2x-8)=2x(-4x+16) | | -175=5(7b-7) | | 4n+8n=6(1+3n)+3(4-8n) | | -2x+17+6x=-8+3x+-4x | | -2x+18+6x=-8+3x+-4x | | 14x-5x=6 | | -7-9(1+6.5y)=18.5 | | 2x+11=-4 | | 6a^2-12ab+6b^2=0 | | -102+x=129-10x | | 5u^2+3u-36=0 | | (11+n)(10+n)(9+n)(8+n)(7+n)(6+n)(5+n)(4+n)(3+n)(2+n)=0 | | 25=-3x+10 | | -3(1-7r)=-150 | | 0.7=m-1.8 | | 5r=45-15 | | 4a^2+8ab-12b^2=0 | | -12x=-132 | | -6y-6= | | 6n^2-6n-120=0 | | 2x+x/3=28 | | -158=-10n+2 | | x^2=1.8x | | f^2+11f+18= | | 2x+1/3x=28 | | 158=-10n+2 |