(7+n)(6+n)(5+n)(4+n)(3+n)(2+n)(n-1)(n-2)(n-3)=0

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Solution for (7+n)(6+n)(5+n)(4+n)(3+n)(2+n)(n-1)(n-2)(n-3)=0 equation:

Simplifying
(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(n + -1)(n + -2)(n + -3) = 0

Reorder the terms:
(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(n + -2)(n + -3) = 0

Reorder the terms:
(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(n + -3) = 0

Reorder the terms:
(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0

Multiply (7 + n) * (6 + n)
(7(6 + n) + n(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
((6 * 7 + n * 7) + n(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
((42 + 7n) + n(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(42 + 7n + (6 * n + n * n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(42 + 7n + (6n + n²))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0

Combine like terms: 7n + 6n = 13n
(42 + 13n + n²)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0

Multiply (42 + 13n + n²) * (5 + n)
(42(5 + n) + 13n * (5 + n) + n²(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
((5 * 42 + n * 42) + 13n * (5 + n) + n²(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
((210 + 42n) + 13n * (5 + n) + n²(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(210 + 42n + (5 * 13n + n * 13n) + n²(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(210 + 42n + (65n + 13n²) + n²(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(210 + 42n + 65n + 13n² + (5 * n² + n * n²))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(210 + 42n + 65n + 13n² + (5n² + n³))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0

Combine like terms: 42n + 65n = 107n
(210 + 107n + 13n² + 5n² + n³)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0

Combine like terms: 13n² + 5n² = 18n²
(210 + 107n + 18n² + n³)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0

Multiply (210 + 107n + 18n² + n³) * (4 + n)
(210(4 + n) + 107n * (4 + n) + 18n² * (4 + n) + n³(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
((4 * 210 + n * 210) + 107n * (4 + n) + 18n² * (4 + n) + n³(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
((840 + 210n) + 107n * (4 + n) + 18n² * (4 + n) + n³(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(840 + 210n + (4 * 107n + n * 107n) + 18n² * (4 + n) + n³(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(840 + 210n + (428n + 107n²) + 18n² * (4 + n) + n³(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(840 + 210n + 428n + 107n² + (4 * 18n² + n * 18n²) + n³(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(840 + 210n + 428n + 107n² + (72n² + 18n³) + n³(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(840 + 210n + 428n + 107n² + 72n² + 18n³ + (4 * n³ + n * n³))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(840 + 210n + 428n + 107n² + 72n² + 18n³ + (4n³ + n⁴))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0

Combine like terms: 210n + 428n = 638n
(840 + 638n + 107n² + 72n² + 18n³ + 4n³ + n⁴)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0

Combine like terms: 107n² + 72n² = 179n²
(840 + 638n + 179n² + 18n³ + 4n³ + n⁴)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0

Combine like terms: 18n³ + 4n³ = 22n³
(840 + 638n + 179n² + 22n³ + n⁴)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0

Multiply (840 + 638n + 179n² + 22n³ + n⁴) * (3 + n)
(840(3 + n) + 638n * (3 + n) + 179n² * (3 + n) + 22n³ * (3 + n) + n⁴(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
((3 * 840 + n * 840) + 638n * (3 + n) + 179n² * (3 + n) + 22n³ * (3 + n) + n⁴(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
((2520 + 840n) + 638n * (3 + n) + 179n² * (3 + n) + 22n³ * (3 + n) + n⁴(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(2520 + 840n + (3 * 638n + n * 638n) + 179n² * (3 + n) + 22n³ * (3 + n) + n⁴(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(2520 + 840n + (1914n + 638n²) + 179n² * (3 + n) + 22n³ * (3 + n) + n⁴(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(2520 + 840n + 1914n + 638n² + (3 * 179n² + n * 179n²) + 22n³ * (3 + n) + n⁴(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(2520 + 840n + 1914n + 638n² + (537n² + 179n³) + 22n³ * (3 + n) + n⁴(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(2520 + 840n + 1914n + 638n² + 537n² + 179n³ + (3 * 22n³ + n * 22n³) + n⁴(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(2520 + 840n + 1914n + 638n² + 537n² + 179n³ + (66n³ + 22n⁴) + n⁴(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(2520 + 840n + 1914n + 638n² + 537n² + 179n³ + 66n³ + 22n⁴ + (3 * n⁴ + n * n⁴))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0
(2520 + 840n + 1914n + 638n² + 537n² + 179n³ + 66n³ + 22n⁴ + (3n⁴ + n⁵))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0

Combine like terms: 840n + 1914n = 2754n
(2520 + 2754n + 638n² + 537n² + 179n³ + 66n³ + 22n⁴ + 3n⁴ + n⁵)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0

Combine like terms: 638n² + 537n² = 1175n²
(2520 + 2754n + 1175n² + 179n³ + 66n³ + 22n⁴ + 3n⁴ + n⁵)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0

Combine like terms: 179n³ + 66n³ = 245n³
(2520 + 2754n + 1175n² + 245n³ + 22n⁴ + 3n⁴ + n⁵)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0

Combine like terms: 22n⁴ + 3n⁴ = 25n⁴
(2520 + 2754n + 1175n² + 245n³ + 25n⁴ + n⁵)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0

Multiply (2520 + 2754n + 1175n² + 245n³ + 25n⁴ + n⁵) * (2 + n)
(2520(2 + n) + 2754n * (2 + n) + 1175n² * (2 + n) + 245n³ * (2 + n) + 25n⁴ * (2 + n) + n⁵(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0
((2 * 2520 + n * 2520) + 2754n * (2 + n) + 1175n² * (2 + n) + 245n³ * (2 + n) + 25n⁴ * (2 + n) + n⁵(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0
((5040 + 2520n) + 2754n * (2 + n) + 1175n² * (2 + n) + 245n³ * (2 + n) + 25n⁴ * (2 + n) + n⁵(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0
(5040 + 2520n + (2 * 2754n + n * 2754n) + 1175n² * (2 + n) + 245n³ * (2 + n) + 25n⁴ * (2 + n) + n⁵(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0
(5040 + 2520n + (5508n + 2754n²) + 1175n² * (2 + n) + 245n³ * (2 + n) + 25n⁴ * (2 + n) + n⁵(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0
(5040 + 2520n + 5508n + 2754n² + (2 * 1175n² + n * 1175n²) + 245n³ * (2 + n) + 25n⁴ * (2 + n) + n⁵(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0
(5040 + 2520n + 5508n + 2754n² + (2350n² + 1175n³) + 245n³ * (2 + n) + 25n⁴ * (2 + n) + n⁵(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0
(5040 + 2520n + 5508n + 2754n² + 2350n² + 1175n³ + (2 * 245n³ + n * 245n³) + 25n⁴ * (2 + n) + n⁵(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0
(5040 + 2520n + 5508n + 2754n² + 2350n² + 1175n³ + (490n³ + 245n⁴) + 25n⁴ * (2 + n) + n⁵(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0
(5040 + 2520n + 5508n + 2754n² + 2350n² + 1175n³ + 490n³ + 245n⁴ + (2 * 25n⁴ + n * 25n⁴) + n⁵(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0
(5040 + 2520n + 5508n + 2754n² + 2350n² + 1175n³ + 490n³ + 245n⁴ + (50n⁴ + 25n⁵) + n⁵(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0
(5040 + 2520n + 5508n + 2754n² + 2350n² + 1175n³ + 490n³ + 245n⁴ + 50n⁴ + 25n⁵ + (2 * n⁵ + n * n⁵))(-1 + n)(-2 + n)(-3 + n) = 0
(5040 + 2520n + 5508n + 2754n² + 2350n² + 1175n³ + 490n³ + 245n⁴ + 50n⁴ + 25n⁵ + (2n⁵ + n⁶))(-1 + n)(-2 + n)(-3 + n) = 0

Combine like terms: 2520n + 5508n = 8028n
(5040 + 8028n + 2754n² + 2350n² + 1175n³ + 490n³ + 245n⁴ + 50n⁴ + 25n⁵ + 2n⁵ + n⁶)(-1 + n)(-2 + n)(-3 + n) = 0

Combine like terms: 2754n² + 2350n² = 5104n²
(5040 + 8028n + 5104n² + 1175n³ + 490n³ + 245n⁴ + 50n⁴ + 25n⁵ + 2n⁵ + n⁶)(-1 + n)(-2 + n)(-3 + n) = 0

Combine like terms: 1175n³ + 490n³ = 1665n³
(5040 + 8028n + 5104n² + 1665n³ + 245n⁴ + 50n⁴ + 25n⁵ + 2n⁵ + n⁶)(-1 + n)(-2 + n)(-3 + n) = 0

Combine like terms: 245n⁴ + 50n⁴ = 295n⁴
(5040 + 8028n + 5104n² + 1665n³ + 295n⁴ + 25n⁵ + 2n⁵ + n⁶)(-1 + n)(-2 + n)(-3 + n) = 0

Combine like terms: 25n⁵ + 2n⁵ = 27n⁵
(5040 + 8028n + 5104n² + 1665n³ + 295n⁴ + 27n⁵ + n⁶)(-1 + n)(-2 + n)(-3 + n) = 0

Multiply (5040 + 8028n + 5104n² + 1665n³ + 295n⁴ + 27n⁵ + n⁶) * (-1 + n)
(5040(-1 + n) + 8028n * (-1 + n) + 5104n² * (-1 + n) + 1665n³ * (-1 + n) + 295n⁴ * (-1 + n) + 27n⁵ * (-1 + n) + n⁶(-1 + n))(-2 + n)(-3 + n) = 0
((-1 * 5040 + n * 5040) + 8028n * (-1 + n) + 5104n² * (-1 + n) + 1665n³ * (-1 + n) + 295n⁴ * (-1 + n) + 27n⁵ * (-1 + n) + n⁶(-1 + n))(-2 + n)(-3 + n) = 0
((-5040 + 5040n) + 8028n * (-1 + n) + 5104n² * (-1 + n) + 1665n³ * (-1 + n) + 295n⁴ * (-1 + n) + 27n⁵ * (-1 + n) + n⁶(-1 + n))(-2 + n)(-3 + n) = 0
(-5040 + 5040n + (-1 * 8028n + n * 8028n) + 5104n² * (-1 + n) + 1665n³ * (-1 + n) + 295n⁴ * (-1 + n) + 27n⁵ * (-1 + n) + n⁶(-1 + n))(-2 + n)(-3 + n) = 0
(-5040 + 5040n + (-8028n + 8028n²) + 5104n² * (-1 + n) + 1665n³ * (-1 + n) + 295n⁴ * (-1 + n) + 27n⁵ * (-1 + n) + n⁶(-1 + n))(-2 + n)(-3 + n) = 0
(-5040 + 5040n + -8028n + 8028n² + (-1 * 5104n² + n * 5104n²) + 1665n³ * (-1 + n) + 295n⁴ * (-1 + n) + 27n⁵ * (-1 + n) + n⁶(-1 + n))(-2 + n)(-3 + n) = 0
(-5040 + 5040n + -8028n + 8028n² + (-5104n² + 5104n³) + 1665n³ * (-1 + n) + 295n⁴ * (-1 + n) + 27n⁵ * (-1 + n) + n⁶(-1 + n))(-2 + n)(-3 + n) = 0
(-5040 + 5040n + -8028n + 8028n² + -5104n² + 5104n³ + (-1 * 1665n³ + n * 1665n³) + 295n⁴ * (-1 + n) + 27n⁵ * (-1 + n) + n⁶(-1 + n))(-2 + n)(-3 + n) = 0
(-5040 + 5040n + -8028n + 8028n² + -5104n² + 5104n³ + (-1665n³ + 1665n⁴) + 295n⁴ * (-1 + n) + 27n⁵ * (-1 + n) + n⁶(-1 + n))(-2 + n)(-3 + n) = 0
(-5040 + 5040n + -8028n + 8028n² + -5104n² + 5104n³ + -1665n³ + 1665n⁴ + (-1 * 295n⁴ + n * 295n⁴) + 27n⁵ * (-1 + n) + n⁶(-1 + n))(-2 + n)(-3 + n) = 0
(-5040 + 5040n + -8028n + 8028n² + -5104n² + 5104n³ + -1665n³ + 1665n⁴ + (-295n⁴ + 295n⁵) + 27n⁵ * (-1 + n) + n⁶(-1 + n))(-2 + n)(-3 + n) = 0
(-5040 + 5040n + -8028n + 8028n² + -5104n² + 5104n³ + -1665n³ + 1665n⁴ + -295n⁴ + 295n⁵ + (-1 * 27n⁵ + n * 27n⁵) + n⁶(-1 + n))(-2 + n)(-3 + n) = 0
(-5040 + 5040n + -8028n + 8028n² + -5104n² + 5104n³ + -1665n³ + 1665n⁴ + -295n⁴ + 295n⁵ + (-27n⁵ + 27n⁶) + n⁶(-1 + n))(-2 + n)(-3 + n) = 0
(-5040 + 5040n + -8028n + 8028n² + -5104n² + 5104n³ + -1665n³ + 1665n⁴ + -295n⁴ + 295n⁵ + -27n⁵ + 27n⁶ + (-1 * n⁶ + n * n⁶))(-2 + n)(-3 + n) = 0
(-5040 + 5040n + -8028n + 8028n² + -5104n² + 5104n³ + -1665n³ + 1665n⁴ + -295n⁴ + 295n⁵ + -27n⁵ + 27n⁶ + (-1n⁶ + n⁷))(-2 + n)(-3 + n) = 0

Combine like terms: 5040n + -8028n = -2988n
(-5040 + -2988n + 8028n² + -5104n² + 5104n³ + -1665n³ + 1665n⁴ + -295n⁴ + 295n⁵ + -27n⁵ + 27n⁶ + -1n⁶ + n⁷)(-2 + n)(-3 + n) = 0

Combine like terms: 8028n² + -5104n² = 2924n²
(-5040 + -2988n + 2924n² + 5104n³ + -1665n³ + 1665n⁴ + -295n⁴ + 295n⁵ + -27n⁵ + 27n⁶ + -1n⁶ + n⁷)(-2 + n)(-3 + n) = 0

Combine like terms: 5104n³ + -1665n³ = 3439n³
(-5040 + -2988n + 2924n² + 3439n³ + 1665n⁴ + -295n⁴ + 295n⁵ + -27n⁵ + 27n⁶ + -1n⁶ + n⁷)(-2 + n)(-3 + n) = 0

Combine like terms: 1665n⁴ + -295n⁴ = 1370n⁴
(-5040 + -2988n + 2924n² + 3439n³ + 1370n⁴ + 295n⁵ + -27n⁵ + 27n⁶ + -1n⁶ + n⁷)(-2 + n)(-3 + n) = 0

Combine like terms: 295n⁵ + -27n⁵ = 268n⁵
(-5040 + -2988n + 2924n² + 3439n³ + 1370n⁴ + 268n⁵ + 27n⁶ + -1n⁶ + n⁷)(-2 + n)(-3 + n) = 0

Combine like terms: 27n⁶ + -1n⁶ = 26n⁶
(-5040 + -2988n + 2924n² + 3439n³ + 1370n⁴ + 268n⁵ + 26n⁶ + n⁷)(-2 + n)(-3 + n) = 0

Multiply (-5040 + -2988n + 2924n² + 3439n³ + 1370n⁴ + 268n⁵ + 26n⁶ + n⁷) * (-2 + n)
(-5040(-2 + n) + -2988n * (-2 + n) + 2924n² * (-2 + n) + 3439n³ * (-2 + n) + 1370n⁴ * (-2 + n) + 268n⁵ * (-2 + n) + 26n⁶ * (-2 + n) + n⁷(-2 + n))(-3 + n) = 0
((-2 * -5040 + n * -5040) + -2988n * (-2 + n) + 2924n² * (-2 + n) + 3439n³ * (-2 + n) + 1370n⁴ * (-2 + n) + 268n⁵ * (-2 + n) + 26n⁶ * (-2 + n) + n⁷(-2 + n))(-3 + n) = 0
((10080 + -5040n) + -2988n * (-2 + n) + 2924n² * (-2 + n) + 3439n³ * (-2 + n) + 1370n⁴ * (-2 + n) + 268n⁵ * (-2 + n) + 26n⁶ * (-2 + n) + n⁷(-2 + n))(-3 + n) = 0
(10080 + -5040n + (-2 * -2988n + n * -2988n) + 2924n² * (-2 + n) + 3439n³ * (-2 + n) + 1370n⁴ * (-2 + n) + 268n⁵ * (-2 + n) + 26n⁶ * (-2 + n) + n⁷(-2 + n))(-3 + n) = 0
(10080 + -5040n + (5976n + -2988n²) + 2924n² * (-2 + n) + 3439n³ * (-2 + n) + 1370n⁴ * (-2 + n) + 268n⁵ * (-2 + n) + 26n⁶ * (-2 + n) + n⁷(-2 + n))(-3 + n) = 0
(10080 + -5040n + 5976n + -2988n² + (-2 * 2924n² + n * 2924n²) + 3439n³ * (-2 + n) + 1370n⁴ * (-2 + n) + 268n⁵ * (-2 + n) + 26n⁶ * (-2 + n) + n⁷(-2 + n))(-3 + n) = 0
(10080 + -5040n + 5976n + -2988n² + (-5848n² + 2924n³) + 3439n³ * (-2 + n) + 1370n⁴ * (-2 + n) + 268n⁵ * (-2 + n) + 26n⁶ * (-2 + n) + n⁷(-2 + n))(-3 + n) = 0
(10080 + -5040n + 5976n + -2988n² + -5848n² + 2924n³ + (-2 * 3439n³ + n * 3439n³) + 1370n⁴ * (-2 + n) + 268n⁵ * (-2 + n) + 26n⁶ * (-2 + n) + n⁷(-2 + n))(-3 + n) = 0
(10080 + -5040n + 5976n + -2988n² + -5848n² + 2924n³ + (-6878n³ + 3439n⁴) + 1370n⁴ * (-2 + n) + 268n⁵ * (-2 + n) + 26n⁶ * (-2 + n) + n⁷(-2 + n))(-3 + n) = 0
(10080 + -5040n + 5976n + -2988n² + -5848n² + 2924n³ + -6878n³ + 3439n⁴ + (-2 * 1370n⁴ + n * 1370n⁴) + 268n⁵ * (-2 + n) + 26n⁶ * (-2 + n) + n⁷(-2 + n))(-3 + n) = 0
(10080 + -5040n + 5976n + -2988n² + -5848n² + 2924n³ + -6878n³ + 3439n⁴ + (-2740n⁴ + 1370n⁵) + 268n⁵ * (-2 + n) + 26n⁶ * (-2 + n) + n⁷(-2 + n))(-3 + n) = 0
(10080 + -5040n + 5976n + -2988n² + -5848n² + 2924n³ + -6878n³ + 3439n⁴ + -2740n⁴ + 1370n⁵ + (-2 * 268n⁵ + n * 268n⁵) + 26n⁶ * (-2 + n) + n⁷(-2 + n))(-3 + n) = 0
(10080 + -5040n + 5976n + -2988n² + -5848n² + 2924n³ + -6878n³ + 3439n⁴ + -2740n⁴ + 1370n⁵ + (-536n⁵ + 268n⁶) + 26n⁶ * (-2 + n) + n⁷(-2 + n))(-3 + n) = 0
(10080 + -5040n + 5976n + -2988n² + -5848n² + 2924n³ + -6878n³ + 3439n⁴ + -2740n⁴ + 1370n⁵ + -536n⁵ + 268n⁶ + (-2 * 26n⁶ + n * 26n⁶) + n⁷(-2 + n))(-3 + n) = 0
(10080 + -5040n + 5976n + -2988n² + -5848n² + 2924n³ + -6878n³ + 3439n⁴ + -2740n⁴ + 1370n⁵ + -536n⁵ + 268n⁶ + (-52n⁶ + 26n⁷) + n⁷(-2 + n))(-3 + n) = 0
(10080 + -5040n + 5976n + -2988n² + -5848n² + 2924n³ + -6878n³ + 3439n⁴ + -2740n⁴ + 1370n⁵ + -536n⁵ + 268n⁶ + -52n⁶ + 26n⁷ + (-2 * n⁷ + n * n⁷))(-3 + n) = 0
(10080 + -5040n + 5976n + -2988n² + -5848n² + 2924n³ + -6878n³ + 3439n⁴ + -2740n⁴ + 1370n⁵ + -536n⁵ + 268n⁶ + -52n⁶ + 26n⁷ + (-2n⁷ + n⁸))(-3 + n) = 0

Combine like terms: -5040n + 5976n = 936n
(10080 + 936n + -2988n² + -5848n² + 2924n³ + -6878n³ + 3439n⁴ + -2740n⁴ + 1370n⁵ + -536n⁵ + 268n⁶ + -52n⁶ + 26n⁷ + -2n⁷ + n⁸)(-3 + n) = 0

Combine like terms: -2988n² + -5848n² = -8836n²
(10080 + 936n + -8836n² + 2924n³ + -6878n³ + 3439n⁴ + -2740n⁴ + 1370n⁵ + -536n⁵ + 268n⁶ + -52n⁶ + 26n⁷ + -2n⁷ + n⁸)(-3 + n) = 0

Combine like terms: 2924n³ + -6878n³ = -3954n³
(10080 + 936n + -8836n² + -3954n³ + 3439n⁴ + -2740n⁴ + 1370n⁵ + -536n⁵ + 268n⁶ + -52n⁶ + 26n⁷ + -2n⁷ + n⁸)(-3 + n) = 0

Combine like terms: 3439n⁴ + -2740n⁴ = 699n⁴
(10080 + 936n + -8836n² + -3954n³ + 699n⁴ + 1370n⁵ + -536n⁵ + 268n⁶ + -52n⁶ + 26n⁷ + -2n⁷ + n⁸)(-3 + n) = 0

Combine like terms: 1370n⁵ + -536n⁵ = 834n⁵
(10080 + 936n + -8836n² + -3954n³ + 699n⁴ + 834n⁵ + 268n⁶ + -52n⁶ + 26n⁷ + -2n⁷ + n⁸)(-3 + n) = 0

Combine like terms: 268n⁶ + -52n⁶ = 216n⁶
(10080 + 936n + -8836n² + -3954n³ + 699n⁴ + 834n⁵ + 216n⁶ + 26n⁷ + -2n⁷ + n⁸)(-3 + n) = 0

Combine like terms: 26n⁷ + -2n⁷ = 24n⁷
(10080 + 936n + -8836n² + -3954n³ + 699n⁴ + 834n⁵ + 216n⁶ + 24n⁷ + n⁸)(-3 + n) = 0

Multiply (10080 + 936n + -8836n² + -3954n³ + 699n⁴ + 834n⁵ + 216n⁶ + 24n⁷ + n⁸) * (-3 + n)
(10080(-3 + n) + 936n * (-3 + n) + -8836n² * (-3 + n) + -3954n³ * (-3 + n) + 699n⁴ * (-3 + n) + 834n⁵ * (-3 + n) + 216n⁶ * (-3 + n) + 24n⁷ * (-3 + n) + n⁸(-3 + n)) = 0
((-3 * 10080 + n * 10080) + 936n * (-3 + n) + -8836n² * (-3 + n) + -3954n³ * (-3 + n) + 699n⁴ * (-3 + n) + 834n⁵ * (-3 + n) + 216n⁶ * (-3 + n) + 24n⁷ * (-3 + n) + n⁸(-3 + n)) = 0
((-30240 + 10080n) + 936n * (-3 + n) + -8836n² * (-3 + n) + -3954n³ * (-3 + n) + 699n⁴ * (-3 + n) + 834n⁵ * (-3 + n) + 216n⁶ * (-3 + n) + 24n⁷ * (-3 + n) + n⁸(-3 + n)) = 0
(-30240 + 10080n + (-3 * 936n + n * 936n) + -8836n² * (-3 + n) + -3954n³ * (-3 + n) + 699n⁴ * (-3 + n) + 834n⁵ * (-3 + n) + 216n⁶ * (-3 + n) + 24n⁷ * (-3 + n) + n⁸(-3 + n)) = 0
(-30240 + 10080n + (-2808n + 936n²) + -8836n² * (-3 + n) + -3954n³ * (-3 + n) + 699n⁴ * (-3 + n) + 834n⁵ * (-3 + n) + 216n⁶ * (-3 + n) + 24n⁷ * (-3 + n) + n⁸(-3 + n)) = 0
(-30240 + 10080n + -2808n + 936n² + (-3 * -8836n² + n * -8836n²) + -3954n³ * (-3 + n) + 699n⁴ * (-3 + n) + 834n⁵ * (-3 + n) + 216n⁶ * (-3 + n) + 24n⁷ * (-3 + n) + n⁸(-3 + n)) = 0
(-30240 + 10080n + -2808n + 936n² + (26508n² + -8836n³) + -3954n³ * (-3 + n) + 699n⁴ * (-3 + n) + 834n⁵ * (-3 + n) + 216n⁶ * (-3 + n) + 24n⁷ * (-3 + n) + n⁸(-3 + n)) = 0
(-30240 + 10080n + -2808n + 936n² + 26508n² + -8836n³ + (-3 * -3954n³ + n * -3954n³) + 699n⁴ * (-3 + n) + 834n⁵ * (-3 + n) + 216n⁶ * (-3 + n) + 24n⁷ * (-3 + n) + n⁸(-3 + n)) = 0
(-30240 + 10080n + -2808n + 936n² + 26508n² + -8836n³ + (11862n³ + -3954n⁴) + 699n⁴ * (-3 + n) + 834n⁵ * (-3 + n) + 216n⁶ * (-3 + n) + 24n⁷ * (-3 + n) + n⁸(-3 + n)) = 0
(-30240 + 10080n + -2808n + 936n² + 26508n² + -8836n³ + 11862n³ + -3954n⁴ + (-3 * 699n⁴ + n * 699n⁴) + 834n⁵ * (-3 + n) + 216n⁶ * (-3 + n) + 24n⁷ * (-3 + n) + n⁸(-3 + n)) = 0
(-30240 + 10080n + -2808n + 936n² + 26508n² + -8836n³ + 11862n³ + -3954n⁴ + (-2097n⁴ + 699n⁵) + 834n⁵ * (-3 + n) + 216n⁶ * (-3 + n) + 24n⁷ * (-3 + n) + n⁸(-3 + n)) = 0
(-30240 + 10080n + -2808n + 936n² + 26508n² + -8836n³ + 11862n³ + -3954n⁴ + -2097n⁴ + 699n⁵ + (-3 * 834n⁵ + n * 834n⁵) + 216n⁶ * (-3 + n) + 24n⁷ * (-3 + n) + n⁸(-3 + n)) = 0
(-30240 + 10080n + -2808n + 936n² + 26508n² + -8836n³ + 11862n³ + -3954n⁴ + -2097n⁴ + 699n⁵ + (-2502n⁵ + 834n⁶) + 216n⁶ * (-3 + n) + 24n⁷ * (-3 + n) + n⁸(-3 + n)) = 0
(-30240 + 10080n + -2808n + 936n² + 26508n² + -8836n³ + 11862n³ + -3954n⁴ + -2097n⁴ + 699n⁵ + -2502n⁵ + 834n⁶ + (-3 * 216n⁶ + n * 216n⁶) + 24n⁷ * (-3 + n) + n⁸(-3 + n)) = 0
(-30240 + 10080n + -2808n + 936n² + 26508n² + -8836n³ + 11862n³ + -3954n⁴ + -2097n⁴ + 699n⁵ + -2502n⁵ + 834n⁶ + (-648n⁶ + 216n⁷) + 24n⁷ * (-3 + n) + n⁸(-3 + n)) = 0
(-30240 + 10080n + -2808n + 936n² + 26508n² + -8836n³ + 11862n³ + -3954n⁴ + -2097n⁴ + 699n⁵ + -2502n⁵ + 834n⁶ + -648n⁶ + 216n⁷ + (-3 * 24n⁷ + n * 24n⁷) + n⁸(-3 + n)) = 0
(-30240 + 10080n + -2808n + 936n² + 26508n² + -8836n³ + 11862n³ + -3954n⁴ + -2097n⁴ + 699n⁵ + -2502n⁵ + 834n⁶ + -648n⁶ + 216n⁷ + (-72n⁷ + 24n⁸) + n⁸(-3 + n)) = 0
(-30240 + 10080n + -2808n + 936n² + 26508n² + -8836n³ + 11862n³ + -3954n⁴ + -2097n⁴ + 699n⁵ + -2502n⁵ + 834n⁶ + -648n⁶ + 216n⁷ + -72n⁷ + 24n⁸ + (-3 * n⁸ + n * n⁸)) = 0
(-30240 + 10080n + -2808n + 936n² + 26508n² + -8836n³ + 11862n³ + -3954n⁴ + -2097n⁴ + 699n⁵ + -2502n⁵ + 834n⁶ + -648n⁶ + 216n⁷ + -72n⁷ + 24n⁸ + (-3n⁸ + n⁹)) = 0

Combine like terms: 10080n + -2808n = 7272n
(-30240 + 7272n + 936n² + 26508n² + -8836n³ + 11862n³ + -3954n⁴ + -2097n⁴ + 699n⁵ + -2502n⁵ + 834n⁶ + -648n⁶ + 216n⁷ + -72n⁷ + 24n⁸ + -3n⁸ + n⁹) = 0

Combine like terms: 936n² + 26508n² = 27444n²
(-30240 + 7272n + 27444n² + -8836n³ + 11862n³ + -3954n⁴ + -2097n⁴ + 699n⁵ + -2502n⁵ + 834n⁶ + -648n⁶ + 216n⁷ + -72n⁷ + 24n⁸ + -3n⁸ + n⁹) = 0

Combine like terms: -8836n³ + 11862n³ = 3026n³
(-30240 + 7272n + 27444n² + 3026n³ + -3954n⁴ + -2097n⁴ + 699n⁵ + -2502n⁵ + 834n⁶ + -648n⁶ + 216n⁷ + -72n⁷ + 24n⁸ + -3n⁸ + n⁹) = 0

Combine like terms: -3954n⁴ + -2097n⁴ = -6051n⁴
(-30240 + 7272n + 27444n² + 3026n³ + -6051n⁴ + 699n⁵ + -2502n⁵ + 834n⁶ + -648n⁶ + 216n⁷ + -72n⁷ + 24n⁸ + -3n⁸ + n⁹) = 0

Combine like terms: 699n⁵ + -2502n⁵ = -1803n⁵
(-30240 + 7272n + 27444n² + 3026n³ + -6051n⁴ + -1803n⁵ + 834n⁶ + -648n⁶ + 216n⁷ + -72n⁷ + 24n⁸ + -3n⁸ + n⁹) = 0

Combine like terms: 834n⁶ + -648n⁶ = 186n⁶
(-30240 + 7272n + 27444n² + 3026n³ + -6051n⁴ + -1803n⁵ + 186n⁶ + 216n⁷ + -72n⁷ + 24n⁸ + -3n⁸ + n⁹) = 0

Combine like terms: 216n⁷ + -72n⁷ = 144n⁷
(-30240 + 7272n + 27444n² + 3026n³ + -6051n⁴ + -1803n⁵ + 186n⁶ + 144n⁷ + 24n⁸ + -3n⁸ + n⁹) = 0

Combine like terms: 24n⁸ + -3n⁸ = 21n⁸
(-30240 + 7272n + 27444n² + 3026n³ + -6051n⁴ + -1803n⁵ + 186n⁶ + 144n⁷ + 21n⁸ + n⁹) = 0

Solving
-30240 + 7272n + 27444n² + 3026n³ + -6051n⁴ + -1803n⁵ + 186n⁶ + 144n⁷ + 21n⁸ + n⁹ = 0

Solving for variable 'n'.

The solution to this equation could not be determined.
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(7+n)(6+n)(5+n)(4+n)(3+n)(2+n)(n-1)(n-2)(n-3)=0

Simple and best practice solution for (7+n)(6+n)(5+n)(4+n)(3+n)(2+n)(n-1)(n-2)(n-3)=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

Solution for (7+n)(6+n)(5+n)(4+n)(3+n)(2+n)(n-1)(n-2)(n-3)=0 equation:

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