3(n+1)(n+2)-(n-1)(n+1)(n+2)=3(n+1)

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Solution for 3(n+1)(n+2)-(n-1)(n+1)(n+2)=3(n+1) equation: 


Simplifying
3(n + 1)(n + 2) + -1(n + -1)(n + 1)(n + 2) = 3(n + 1)

Reorder the terms:
3(1 + n)(n + 2) + -1(n + -1)(n + 1)(n + 2) = 3(n + 1)

Reorder the terms:
3(1 + n)(2 + n) + -1(n + -1)(n + 1)(n + 2) = 3(n + 1)

Multiply (1 + n) * (2 + n)
3(1(2 + n) + n(2 + n)) + -1(n + -1)(n + 1)(n + 2) = 3(n + 1)
3((2 * 1 + n * 1) + n(2 + n)) + -1(n + -1)(n + 1)(n + 2) = 3(n + 1)
3((2 + 1n) + n(2 + n)) + -1(n + -1)(n + 1)(n + 2) = 3(n + 1)
3(2 + 1n + (2 * n + n * n)) + -1(n + -1)(n + 1)(n + 2) = 3(n + 1)
3(2 + 1n + (2n + n2)) + -1(n + -1)(n + 1)(n + 2) = 3(n + 1)

Combine like terms: 1n + 2n = 3n
3(2 + 3n + n2) + -1(n + -1)(n + 1)(n + 2) = 3(n + 1)
(2 * 3 + 3n * 3 + n2 * 3) + -1(n + -1)(n + 1)(n + 2) = 3(n + 1)
(6 + 9n + 3n2) + -1(n + -1)(n + 1)(n + 2) = 3(n + 1)

Reorder the terms:
6 + 9n + 3n2 + -1(-1 + n)(n + 1)(n + 2) = 3(n + 1)

Reorder the terms:
6 + 9n + 3n2 + -1(-1 + n)(1 + n)(n + 2) = 3(n + 1)

Reorder the terms:
6 + 9n + 3n2 + -1(-1 + n)(1 + n)(2 + n) = 3(n + 1)

Multiply (-1 + n) * (1 + n)
6 + 9n + 3n2 + -1(-1(1 + n) + n(1 + n))(2 + n) = 3(n + 1)
6 + 9n + 3n2 + -1((1 * -1 + n * -1) + n(1 + n))(2 + n) = 3(n + 1)
6 + 9n + 3n2 + -1((-1 + -1n) + n(1 + n))(2 + n) = 3(n + 1)
6 + 9n + 3n2 + -1(-1 + -1n + (1 * n + n * n))(2 + n) = 3(n + 1)
6 + 9n + 3n2 + -1(-1 + -1n + (1n + n2))(2 + n) = 3(n + 1)

Combine like terms: -1n + 1n = 0
6 + 9n + 3n2 + -1(-1 + 0 + n2)(2 + n) = 3(n + 1)
6 + 9n + 3n2 + -1(-1 + n2)(2 + n) = 3(n + 1)

Multiply (-1 + n2) * (2 + n)
6 + 9n + 3n2 + -1(-1(2 + n) + n2(2 + n)) = 3(n + 1)
6 + 9n + 3n2 + -1((2 * -1 + n * -1) + n2(2 + n)) = 3(n + 1)
6 + 9n + 3n2 + -1((-2 + -1n) + n2(2 + n)) = 3(n + 1)
6 + 9n + 3n2 + -1(-2 + -1n + (2 * n2 + n * n2)) = 3(n + 1)
6 + 9n + 3n2 + -1(-2 + -1n + (2n2 + n3)) = 3(n + 1)
6 + 9n + 3n2 + -1(-2 + -1n + 2n2 + n3) = 3(n + 1)
6 + 9n + 3n2 + (-2 * -1 + -1n * -1 + 2n2 * -1 + n3 * -1) = 3(n + 1)
6 + 9n + 3n2 + (2 + 1n + -2n2 + -1n3) = 3(n + 1)

Reorder the terms:
6 + 2 + 9n + 1n + 3n2 + -2n2 + -1n3 = 3(n + 1)

Combine like terms: 6 + 2 = 8
8 + 9n + 1n + 3n2 + -2n2 + -1n3 = 3(n + 1)

Combine like terms: 9n + 1n = 10n
8 + 10n + 3n2 + -2n2 + -1n3 = 3(n + 1)

Combine like terms: 3n2 + -2n2 = 1n2
8 + 10n + 1n2 + -1n3 = 3(n + 1)

Reorder the terms:
8 + 10n + 1n2 + -1n3 = 3(1 + n)
8 + 10n + 1n2 + -1n3 = (1 * 3 + n * 3)
8 + 10n + 1n2 + -1n3 = (3 + 3n)

Solving
8 + 10n + 1n2 + -1n3 = 3 + 3n

Solving for variable 'n'.

Reorder the terms:
8 + -3 + 10n + -3n + 1n2 + -1n3 = 3 + 3n + -3 + -3n

Combine like terms: 8 + -3 = 5
5 + 10n + -3n + 1n2 + -1n3 = 3 + 3n + -3 + -3n

Combine like terms: 10n + -3n = 7n
5 + 7n + 1n2 + -1n3 = 3 + 3n + -3 + -3n

Reorder the terms:
5 + 7n + 1n2 + -1n3 = 3 + -3 + 3n + -3n

Combine like terms: 3 + -3 = 0
5 + 7n + 1n2 + -1n3 = 0 + 3n + -3n
5 + 7n + 1n2 + -1n3 = 3n + -3n

Combine like terms: 3n + -3n = 0
5 + 7n + 1n2 + -1n3 = 0

The solution to this equation could not be determined.

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