(6k+1)(6k+2)(12k+2)=0

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Solution for (6k+1)(6k+2)(12k+2)=0 equation: 


Simplifying
(6k + 1)(6k + 2)(12k + 2) = 0

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

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

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

Multiply (1 + 6k) * (2 + 6k)
(1(2 + 6k) + 6k * (2 + 6k))(2 + 12k) = 0
((2 * 1 + 6k * 1) + 6k * (2 + 6k))(2 + 12k) = 0
((2 + 6k) + 6k * (2 + 6k))(2 + 12k) = 0
(2 + 6k + (2 * 6k + 6k * 6k))(2 + 12k) = 0
(2 + 6k + (12k + 36k2))(2 + 12k) = 0

Combine like terms: 6k + 12k = 18k
(2 + 18k + 36k2)(2 + 12k) = 0

Multiply (2 + 18k + 36k2) * (2 + 12k)
(2(2 + 12k) + 18k * (2 + 12k) + 36k2 * (2 + 12k)) = 0
((2 * 2 + 12k * 2) + 18k * (2 + 12k) + 36k2 * (2 + 12k)) = 0
((4 + 24k) + 18k * (2 + 12k) + 36k2 * (2 + 12k)) = 0
(4 + 24k + (2 * 18k + 12k * 18k) + 36k2 * (2 + 12k)) = 0
(4 + 24k + (36k + 216k2) + 36k2 * (2 + 12k)) = 0
(4 + 24k + 36k + 216k2 + (2 * 36k2 + 12k * 36k2)) = 0
(4 + 24k + 36k + 216k2 + (72k2 + 432k3)) = 0

Combine like terms: 24k + 36k = 60k
(4 + 60k + 216k2 + 72k2 + 432k3) = 0

Combine like terms: 216k2 + 72k2 = 288k2
(4 + 60k + 288k2 + 432k3) = 0

Solving
4 + 60k + 288k2 + 432k3 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 15k + 72k2 + 108k3) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(1 + 15k + 72k2 + 108k3)' equal to zero and attempt to solve:

Simplifying
1 + 15k + 72k2 + 108k3 = 0

Solving
1 + 15k + 72k2 + 108k3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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