(k+1)(k+2)+3(k+1)(k+2)=(k+1)(k+2)(k+3)

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Solution for (k+1)(k+2)+3(k+1)(k+2)=(k+1)(k+2)(k+3) equation: 


Simplifying
(k + 1)(k + 2) + 3(k + 1)(k + 2) = (k + 1)(k + 2)(k + 3)

Reorder the terms:
(1 + k)(k + 2) + 3(k + 1)(k + 2) = (k + 1)(k + 2)(k + 3)

Reorder the terms:
(1 + k)(2 + k) + 3(k + 1)(k + 2) = (k + 1)(k + 2)(k + 3)

Multiply (1 + k) * (2 + k)
(1(2 + k) + k(2 + k)) + 3(k + 1)(k + 2) = (k + 1)(k + 2)(k + 3)
((2 * 1 + k * 1) + k(2 + k)) + 3(k + 1)(k + 2) = (k + 1)(k + 2)(k + 3)
((2 + 1k) + k(2 + k)) + 3(k + 1)(k + 2) = (k + 1)(k + 2)(k + 3)
(2 + 1k + (2 * k + k * k)) + 3(k + 1)(k + 2) = (k + 1)(k + 2)(k + 3)
(2 + 1k + (2k + k2)) + 3(k + 1)(k + 2) = (k + 1)(k + 2)(k + 3)

Combine like terms: 1k + 2k = 3k
(2 + 3k + k2) + 3(k + 1)(k + 2) = (k + 1)(k + 2)(k + 3)

Reorder the terms:
2 + 3k + k2 + 3(1 + k)(k + 2) = (k + 1)(k + 2)(k + 3)

Reorder the terms:
2 + 3k + k2 + 3(1 + k)(2 + k) = (k + 1)(k + 2)(k + 3)

Multiply (1 + k) * (2 + k)
2 + 3k + k2 + 3(1(2 + k) + k(2 + k)) = (k + 1)(k + 2)(k + 3)
2 + 3k + k2 + 3((2 * 1 + k * 1) + k(2 + k)) = (k + 1)(k + 2)(k + 3)
2 + 3k + k2 + 3((2 + 1k) + k(2 + k)) = (k + 1)(k + 2)(k + 3)
2 + 3k + k2 + 3(2 + 1k + (2 * k + k * k)) = (k + 1)(k + 2)(k + 3)
2 + 3k + k2 + 3(2 + 1k + (2k + k2)) = (k + 1)(k + 2)(k + 3)

Combine like terms: 1k + 2k = 3k
2 + 3k + k2 + 3(2 + 3k + k2) = (k + 1)(k + 2)(k + 3)
2 + 3k + k2 + (2 * 3 + 3k * 3 + k2 * 3) = (k + 1)(k + 2)(k + 3)
2 + 3k + k2 + (6 + 9k + 3k2) = (k + 1)(k + 2)(k + 3)

Reorder the terms:
2 + 6 + 3k + 9k + k2 + 3k2 = (k + 1)(k + 2)(k + 3)

Combine like terms: 2 + 6 = 8
8 + 3k + 9k + k2 + 3k2 = (k + 1)(k + 2)(k + 3)

Combine like terms: 3k + 9k = 12k
8 + 12k + k2 + 3k2 = (k + 1)(k + 2)(k + 3)

Combine like terms: k2 + 3k2 = 4k2
8 + 12k + 4k2 = (k + 1)(k + 2)(k + 3)

Reorder the terms:
8 + 12k + 4k2 = (1 + k)(k + 2)(k + 3)

Reorder the terms:
8 + 12k + 4k2 = (1 + k)(2 + k)(k + 3)

Reorder the terms:
8 + 12k + 4k2 = (1 + k)(2 + k)(3 + k)

Multiply (1 + k) * (2 + k)
8 + 12k + 4k2 = (1(2 + k) + k(2 + k))(3 + k)
8 + 12k + 4k2 = ((2 * 1 + k * 1) + k(2 + k))(3 + k)
8 + 12k + 4k2 = ((2 + 1k) + k(2 + k))(3 + k)
8 + 12k + 4k2 = (2 + 1k + (2 * k + k * k))(3 + k)
8 + 12k + 4k2 = (2 + 1k + (2k + k2))(3 + k)

Combine like terms: 1k + 2k = 3k
8 + 12k + 4k2 = (2 + 3k + k2)(3 + k)

Multiply (2 + 3k + k2) * (3 + k)
8 + 12k + 4k2 = (2(3 + k) + 3k * (3 + k) + k2(3 + k))
8 + 12k + 4k2 = ((3 * 2 + k * 2) + 3k * (3 + k) + k2(3 + k))
8 + 12k + 4k2 = ((6 + 2k) + 3k * (3 + k) + k2(3 + k))
8 + 12k + 4k2 = (6 + 2k + (3 * 3k + k * 3k) + k2(3 + k))
8 + 12k + 4k2 = (6 + 2k + (9k + 3k2) + k2(3 + k))
8 + 12k + 4k2 = (6 + 2k + 9k + 3k2 + (3 * k2 + k * k2))
8 + 12k + 4k2 = (6 + 2k + 9k + 3k2 + (3k2 + k3))

Combine like terms: 2k + 9k = 11k
8 + 12k + 4k2 = (6 + 11k + 3k2 + 3k2 + k3)

Combine like terms: 3k2 + 3k2 = 6k2
8 + 12k + 4k2 = (6 + 11k + 6k2 + k3)

Solving
8 + 12k + 4k2 = 6 + 11k + 6k2 + k3

Solving for variable 'k'.

Reorder the terms:
8 + -6 + 12k + -11k + 4k2 + -6k2 + -1k3 = 6 + 11k + 6k2 + k3 + -6 + -11k + -6k2 + -1k3

Combine like terms: 8 + -6 = 2
2 + 12k + -11k + 4k2 + -6k2 + -1k3 = 6 + 11k + 6k2 + k3 + -6 + -11k + -6k2 + -1k3

Combine like terms: 12k + -11k = 1k
2 + 1k + 4k2 + -6k2 + -1k3 = 6 + 11k + 6k2 + k3 + -6 + -11k + -6k2 + -1k3

Combine like terms: 4k2 + -6k2 = -2k2
2 + 1k + -2k2 + -1k3 = 6 + 11k + 6k2 + k3 + -6 + -11k + -6k2 + -1k3

Reorder the terms:
2 + 1k + -2k2 + -1k3 = 6 + -6 + 11k + -11k + 6k2 + -6k2 + k3 + -1k3

Combine like terms: 6 + -6 = 0
2 + 1k + -2k2 + -1k3 = 0 + 11k + -11k + 6k2 + -6k2 + k3 + -1k3
2 + 1k + -2k2 + -1k3 = 11k + -11k + 6k2 + -6k2 + k3 + -1k3

Combine like terms: 11k + -11k = 0
2 + 1k + -2k2 + -1k3 = 0 + 6k2 + -6k2 + k3 + -1k3
2 + 1k + -2k2 + -1k3 = 6k2 + -6k2 + k3 + -1k3

Combine like terms: 6k2 + -6k2 = 0
2 + 1k + -2k2 + -1k3 = 0 + k3 + -1k3
2 + 1k + -2k2 + -1k3 = k3 + -1k3

Combine like terms: k3 + -1k3 = 0
2 + 1k + -2k2 + -1k3 = 0

The solution to this equation could not be determined.

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