k^3+6k^2+11k+6=(k+1)(k+2)(k+3)

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Solution for k^3+6k^2+11k+6=(k+1)(k+2)(k+3) equation: 


Simplifying
k3 + 6k2 + 11k + 6 = (k + 1)(k + 2)(k + 3)

Reorder the terms:
6 + 11k + 6k2 + k3 = (k + 1)(k + 2)(k + 3)

Reorder the terms:
6 + 11k + 6k2 + k3 = (1 + k)(k + 2)(k + 3)

Reorder the terms:
6 + 11k + 6k2 + k3 = (1 + k)(2 + k)(k + 3)

Reorder the terms:
6 + 11k + 6k2 + k3 = (1 + k)(2 + k)(3 + k)

Multiply (1 + k) * (2 + k)
6 + 11k + 6k2 + k3 = (1(2 + k) + k(2 + k))(3 + k)
6 + 11k + 6k2 + k3 = ((2 * 1 + k * 1) + k(2 + k))(3 + k)
6 + 11k + 6k2 + k3 = ((2 + 1k) + k(2 + k))(3 + k)
6 + 11k + 6k2 + k3 = (2 + 1k + (2 * k + k * k))(3 + k)
6 + 11k + 6k2 + k3 = (2 + 1k + (2k + k2))(3 + k)

Combine like terms: 1k + 2k = 3k
6 + 11k + 6k2 + k3 = (2 + 3k + k2)(3 + k)

Multiply (2 + 3k + k2) * (3 + k)
6 + 11k + 6k2 + k3 = (2(3 + k) + 3k * (3 + k) + k2(3 + k))
6 + 11k + 6k2 + k3 = ((3 * 2 + k * 2) + 3k * (3 + k) + k2(3 + k))
6 + 11k + 6k2 + k3 = ((6 + 2k) + 3k * (3 + k) + k2(3 + k))
6 + 11k + 6k2 + k3 = (6 + 2k + (3 * 3k + k * 3k) + k2(3 + k))
6 + 11k + 6k2 + k3 = (6 + 2k + (9k + 3k2) + k2(3 + k))
6 + 11k + 6k2 + k3 = (6 + 2k + 9k + 3k2 + (3 * k2 + k * k2))
6 + 11k + 6k2 + k3 = (6 + 2k + 9k + 3k2 + (3k2 + k3))

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

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

Add '-6' to each side of the equation.
6 + 11k + 6k2 + -6 + k3 = 6 + 11k + 6k2 + -6 + k3

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

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

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

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

Add '-11k' to each side of the equation.
11k + 6k2 + -11k + k3 = 11k + 6k2 + -11k + k3

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

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

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

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

Add '-6k2' to each side of the equation.
6k2 + -6k2 + k3 = 6k2 + -6k2 + k3

Combine like terms: 6k2 + -6k2 = 0
0 + k3 = 6k2 + -6k2 + k3
k3 = 6k2 + -6k2 + k3

Combine like terms: 6k2 + -6k2 = 0
k3 = 0 + k3
k3 = k3

Add '-1k3' to each side of the equation.
k3 + -1k3 = k3 + -1k3

Combine like terms: k3 + -1k3 = 0
0 = k3 + -1k3

Combine like terms: k3 + -1k3 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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