=(k^2+6k)(k^2+2k-24)

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Solution for =(k^2+6k)(k^2+2k-24) equation: 


Simplifying
0 = (k2 + 6k)(k2 + 2k + -24)

Reorder the terms:
0 = (6k + k2)(k2 + 2k + -24)

Reorder the terms:
0 = (6k + k2)(-24 + 2k + k2)

Multiply (6k + k2) * (-24 + 2k + k2)
0 = (6k * (-24 + 2k + k2) + k2(-24 + 2k + k2))
0 = ((-24 * 6k + 2k * 6k + k2 * 6k) + k2(-24 + 2k + k2))
0 = ((-144k + 12k2 + 6k3) + k2(-24 + 2k + k2))
0 = (-144k + 12k2 + 6k3 + (-24 * k2 + 2k * k2 + k2 * k2))
0 = (-144k + 12k2 + 6k3 + (-24k2 + 2k3 + k4))

Reorder the terms:
0 = (-144k + 12k2 + -24k2 + 6k3 + 2k3 + k4)

Combine like terms: 12k2 + -24k2 = -12k2
0 = (-144k + -12k2 + 6k3 + 2k3 + k4)

Combine like terms: 6k3 + 2k3 = 8k3
0 = (-144k + -12k2 + 8k3 + k4)

Solving
0 = -144k + -12k2 + 8k3 + k4

Solving for variable 'k'.
Remove the zero:
144k + 12k2 + -8k3 + -1k4 = -144k + -12k2 + 8k3 + k4 + 144k + 12k2 + -8k3 + -1k4

Reorder the terms:
144k + 12k2 + -8k3 + -1k4 = -144k + 144k + -12k2 + 12k2 + 8k3 + -8k3 + k4 + -1k4

Combine like terms: -144k + 144k = 0
144k + 12k2 + -8k3 + -1k4 = 0 + -12k2 + 12k2 + 8k3 + -8k3 + k4 + -1k4
144k + 12k2 + -8k3 + -1k4 = -12k2 + 12k2 + 8k3 + -8k3 + k4 + -1k4

Combine like terms: -12k2 + 12k2 = 0
144k + 12k2 + -8k3 + -1k4 = 0 + 8k3 + -8k3 + k4 + -1k4
144k + 12k2 + -8k3 + -1k4 = 8k3 + -8k3 + k4 + -1k4

Combine like terms: 8k3 + -8k3 = 0
144k + 12k2 + -8k3 + -1k4 = 0 + k4 + -1k4
144k + 12k2 + -8k3 + -1k4 = k4 + -1k4

Combine like terms: k4 + -1k4 = 0
144k + 12k2 + -8k3 + -1k4 = 0

Factor out the Greatest Common Factor (GCF), 'k'.
k(144 + 12k + -8k2 + -1k3) = 0


Subproblem 1
Set the factor 'k' equal to zero and attempt to solve:

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0

Subproblem 2
Set the factor '(144 + 12k + -8k2 + -1k3)' equal to zero and attempt to solve:

Simplifying
144 + 12k + -8k2 + -1k3 = 0

Solving
144 + 12k + -8k2 + -1k3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
k = {0}

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