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

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

Simplifying
S = n(n + 1)(2n + 1) * 6

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

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

Reorder the terms for easier multiplication:
S = 6n(1 + n)(1 + 2n)

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

Combine like terms: 2n + 1n = 3n
S = 6n(1 + 3n + 2n2)
S = (1 * 6n + 3n * 6n + 2n2 * 6n)
S = (6n + 18n2 + 12n3)

Solving
S = 6n + 18n2 + 12n3

Solving for variable 'S'.

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

Simplifying
S = 6n + 18n2 + 12n3