=(2k+3)(4k^3-3k^2+k)

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Solution for =(2k+3)(4k^3-3k^2+k) equation: 


Simplifying
0 = (2k + 3)(4k3 + -3k2 + k)

Reorder the terms:
0 = (3 + 2k)(4k3 + -3k2 + k)

Reorder the terms:
0 = (3 + 2k)(k + -3k2 + 4k3)

Multiply (3 + 2k) * (k + -3k2 + 4k3)
0 = (3(k + -3k2 + 4k3) + 2k * (k + -3k2 + 4k3))
0 = ((k * 3 + -3k2 * 3 + 4k3 * 3) + 2k * (k + -3k2 + 4k3))
0 = ((3k + -9k2 + 12k3) + 2k * (k + -3k2 + 4k3))
0 = (3k + -9k2 + 12k3 + (k * 2k + -3k2 * 2k + 4k3 * 2k))
0 = (3k + -9k2 + 12k3 + (2k2 + -6k3 + 8k4))

Reorder the terms:
0 = (3k + -9k2 + 2k2 + 12k3 + -6k3 + 8k4)

Combine like terms: -9k2 + 2k2 = -7k2
0 = (3k + -7k2 + 12k3 + -6k3 + 8k4)

Combine like terms: 12k3 + -6k3 = 6k3
0 = (3k + -7k2 + 6k3 + 8k4)

Solving
0 = 3k + -7k2 + 6k3 + 8k4

Solving for variable 'k'.
Remove the zero:
-3k + 7k2 + -6k3 + -8k4 = 3k + -7k2 + 6k3 + 8k4 + -3k + 7k2 + -6k3 + -8k4

Reorder the terms:
-3k + 7k2 + -6k3 + -8k4 = 3k + -3k + -7k2 + 7k2 + 6k3 + -6k3 + 8k4 + -8k4

Combine like terms: 3k + -3k = 0
-3k + 7k2 + -6k3 + -8k4 = 0 + -7k2 + 7k2 + 6k3 + -6k3 + 8k4 + -8k4
-3k + 7k2 + -6k3 + -8k4 = -7k2 + 7k2 + 6k3 + -6k3 + 8k4 + -8k4

Combine like terms: -7k2 + 7k2 = 0
-3k + 7k2 + -6k3 + -8k4 = 0 + 6k3 + -6k3 + 8k4 + -8k4
-3k + 7k2 + -6k3 + -8k4 = 6k3 + -6k3 + 8k4 + -8k4

Combine like terms: 6k3 + -6k3 = 0
-3k + 7k2 + -6k3 + -8k4 = 0 + 8k4 + -8k4
-3k + 7k2 + -6k3 + -8k4 = 8k4 + -8k4

Combine like terms: 8k4 + -8k4 = 0
-3k + 7k2 + -6k3 + -8k4 = 0

Factor out the Greatest Common Factor (GCF), 'k'.
k(-3 + 7k + -6k2 + -8k3) = 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 '(-3 + 7k + -6k2 + -8k3)' equal to zero and attempt to solve:

Simplifying
-3 + 7k + -6k2 + -8k3 = 0

Solving
-3 + 7k + -6k2 + -8k3 = 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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