n(n+1)(6n^5+15n^4+6n^3-6n^2-n+1)(n+7)=0

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Solution for n(n+1)(6n^5+15n^4+6n^3-6n^2-n+1)(n+7)=0 equation: 


Simplifying
n(n + 1)(6n5 + 15n4 + 6n3 + -6n2 + -1n + 1)(n + 7) = 0

Reorder the terms:
n(1 + n)(6n5 + 15n4 + 6n3 + -6n2 + -1n + 1)(n + 7) = 0

Reorder the terms:
n(1 + n)(1 + -1n + -6n2 + 6n3 + 15n4 + 6n5)(n + 7) = 0

Reorder the terms:
n(1 + n)(1 + -1n + -6n2 + 6n3 + 15n4 + 6n5)(7 + n) = 0

Multiply (1 + n) * (1 + -1n + -6n2 + 6n3 + 15n4 + 6n5)
n(1(1 + -1n + -6n2 + 6n3 + 15n4 + 6n5) + n(1 + -1n + -6n2 + 6n3 + 15n4 + 6n5))(7 + n) = 0
n((1 * 1 + -1n * 1 + -6n2 * 1 + 6n3 * 1 + 15n4 * 1 + 6n5 * 1) + n(1 + -1n + -6n2 + 6n3 + 15n4 + 6n5))(7 + n) = 0
n((1 + -1n + -6n2 + 6n3 + 15n4 + 6n5) + n(1 + -1n + -6n2 + 6n3 + 15n4 + 6n5))(7 + n) = 0
n(1 + -1n + -6n2 + 6n3 + 15n4 + 6n5 + (1 * n + -1n * n + -6n2 * n + 6n3 * n + 15n4 * n + 6n5 * n))(7 + n) = 0
n(1 + -1n + -6n2 + 6n3 + 15n4 + 6n5 + (1n + -1n2 + -6n3 + 6n4 + 15n5 + 6n6))(7 + n) = 0

Reorder the terms:
n(1 + -1n + 1n + -6n2 + -1n2 + 6n3 + -6n3 + 15n4 + 6n4 + 6n5 + 15n5 + 6n6)(7 + n) = 0

Combine like terms: -1n + 1n = 0
n(1 + 0 + -6n2 + -1n2 + 6n3 + -6n3 + 15n4 + 6n4 + 6n5 + 15n5 + 6n6)(7 + n) = 0
n(1 + -6n2 + -1n2 + 6n3 + -6n3 + 15n4 + 6n4 + 6n5 + 15n5 + 6n6)(7 + n) = 0

Combine like terms: -6n2 + -1n2 = -7n2
n(1 + -7n2 + 6n3 + -6n3 + 15n4 + 6n4 + 6n5 + 15n5 + 6n6)(7 + n) = 0

Combine like terms: 6n3 + -6n3 = 0
n(1 + -7n2 + 0 + 15n4 + 6n4 + 6n5 + 15n5 + 6n6)(7 + n) = 0
n(1 + -7n2 + 15n4 + 6n4 + 6n5 + 15n5 + 6n6)(7 + n) = 0

Combine like terms: 15n4 + 6n4 = 21n4
n(1 + -7n2 + 21n4 + 6n5 + 15n5 + 6n6)(7 + n) = 0

Combine like terms: 6n5 + 15n5 = 21n5
n(1 + -7n2 + 21n4 + 21n5 + 6n6)(7 + n) = 0

Multiply (1 + -7n2 + 21n4 + 21n5 + 6n6) * (7 + n)
n(1(7 + n) + -7n2 * (7 + n) + 21n4 * (7 + n) + 21n5 * (7 + n) + 6n6 * (7 + n)) = 0
n((7 * 1 + n * 1) + -7n2 * (7 + n) + 21n4 * (7 + n) + 21n5 * (7 + n) + 6n6 * (7 + n)) = 0
n((7 + 1n) + -7n2 * (7 + n) + 21n4 * (7 + n) + 21n5 * (7 + n) + 6n6 * (7 + n)) = 0
n(7 + 1n + (7 * -7n2 + n * -7n2) + 21n4 * (7 + n) + 21n5 * (7 + n) + 6n6 * (7 + n)) = 0
n(7 + 1n + (-49n2 + -7n3) + 21n4 * (7 + n) + 21n5 * (7 + n) + 6n6 * (7 + n)) = 0
n(7 + 1n + -49n2 + -7n3 + (7 * 21n4 + n * 21n4) + 21n5 * (7 + n) + 6n6 * (7 + n)) = 0
n(7 + 1n + -49n2 + -7n3 + (147n4 + 21n5) + 21n5 * (7 + n) + 6n6 * (7 + n)) = 0
n(7 + 1n + -49n2 + -7n3 + 147n4 + 21n5 + (7 * 21n5 + n * 21n5) + 6n6 * (7 + n)) = 0
n(7 + 1n + -49n2 + -7n3 + 147n4 + 21n5 + (147n5 + 21n6) + 6n6 * (7 + n)) = 0
n(7 + 1n + -49n2 + -7n3 + 147n4 + 21n5 + 147n5 + 21n6 + (7 * 6n6 + n * 6n6)) = 0
n(7 + 1n + -49n2 + -7n3 + 147n4 + 21n5 + 147n5 + 21n6 + (42n6 + 6n7)) = 0

Combine like terms: 21n5 + 147n5 = 168n5
n(7 + 1n + -49n2 + -7n3 + 147n4 + 168n5 + 21n6 + 42n6 + 6n7) = 0

Combine like terms: 21n6 + 42n6 = 63n6
n(7 + 1n + -49n2 + -7n3 + 147n4 + 168n5 + 63n6 + 6n7) = 0
(7 * n + 1n * n + -49n2 * n + -7n3 * n + 147n4 * n + 168n5 * n + 63n6 * n + 6n7 * n) = 0
(7n + 1n2 + -49n3 + -7n4 + 147n5 + 168n6 + 63n7 + 6n8) = 0

Solving
7n + 1n2 + -49n3 + -7n4 + 147n5 + 168n6 + 63n7 + 6n8 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(7 + n + -49n2 + -7n3 + 147n4 + 168n5 + 63n6 + 6n7) = 0


Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

Move all terms containing n to the left, all other terms to the right.

Simplifying
n = 0

Subproblem 2
Set the factor '(7 + n + -49n2 + -7n3 + 147n4 + 168n5 + 63n6 + 6n7)' equal to zero and attempt to solve:

Simplifying
7 + n + -49n2 + -7n3 + 147n4 + 168n5 + 63n6 + 6n7 = 0

Solving
7 + n + -49n2 + -7n3 + 147n4 + 168n5 + 63n6 + 6n7 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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