6(n+1)(n+1)+n(n+1)(2n+1)=0

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Solution for 6(n+1)(n+1)+n(n+1)(2n+1)=0 equation: 


Simplifying
6(n + 1)(n + 1) + n(n + 1)(2n + 1) = 0

Reorder the terms:
6(1 + n)(n + 1) + n(n + 1)(2n + 1) = 0

Reorder the terms:
6(1 + n)(1 + n) + n(n + 1)(2n + 1) = 0

Multiply (1 + n) * (1 + n)
6(1(1 + n) + n(1 + n)) + n(n + 1)(2n + 1) = 0
6((1 * 1 + n * 1) + n(1 + n)) + n(n + 1)(2n + 1) = 0
6((1 + 1n) + n(1 + n)) + n(n + 1)(2n + 1) = 0
6(1 + 1n + (1 * n + n * n)) + n(n + 1)(2n + 1) = 0
6(1 + 1n + (1n + n2)) + n(n + 1)(2n + 1) = 0

Combine like terms: 1n + 1n = 2n
6(1 + 2n + n2) + n(n + 1)(2n + 1) = 0
(1 * 6 + 2n * 6 + n2 * 6) + n(n + 1)(2n + 1) = 0
(6 + 12n + 6n2) + n(n + 1)(2n + 1) = 0

Reorder the terms:
6 + 12n + 6n2 + n(1 + n)(2n + 1) = 0

Reorder the terms:
6 + 12n + 6n2 + n(1 + n)(1 + 2n) = 0

Multiply (1 + n) * (1 + 2n)
6 + 12n + 6n2 + n(1(1 + 2n) + n(1 + 2n)) = 0
6 + 12n + 6n2 + n((1 * 1 + 2n * 1) + n(1 + 2n)) = 0
6 + 12n + 6n2 + n((1 + 2n) + n(1 + 2n)) = 0
6 + 12n + 6n2 + n(1 + 2n + (1 * n + 2n * n)) = 0
6 + 12n + 6n2 + n(1 + 2n + (1n + 2n2)) = 0

Combine like terms: 2n + 1n = 3n
6 + 12n + 6n2 + n(1 + 3n + 2n2) = 0
6 + 12n + 6n2 + (1 * n + 3n * n + 2n2 * n) = 0
6 + 12n + 6n2 + (1n + 3n2 + 2n3) = 0

Reorder the terms:
6 + 12n + 1n + 6n2 + 3n2 + 2n3 = 0

Combine like terms: 12n + 1n = 13n
6 + 13n + 6n2 + 3n2 + 2n3 = 0

Combine like terms: 6n2 + 3n2 = 9n2
6 + 13n + 9n2 + 2n3 = 0

Solving
6 + 13n + 9n2 + 2n3 = 0

Solving for variable 'n'.

The solution to this equation could not be determined.

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