12k^3q^4-4k^2q^5-kq^6=0

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Solution for 12k^3q^4-4k^2q^5-kq^6=0 equation: 


Simplifying
12k3q4 + -4k2q5 + -1kq6 = 0

Reorder the terms:
-1kq6 + -4k2q5 + 12k3q4 = 0

Solving
-1kq6 + -4k2q5 + 12k3q4 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'kq4'.
kq4(-1q2 + -4kq + 12k2) = 0

Factor a trinomial.
kq4((-1q + -6k)(q + -2k)) = 0


Subproblem 1
Set the factor 'kq4' equal to zero and attempt to solve:

Simplifying
kq4 = 0

Solving
kq4 = 0

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

Simplifying
kq4 = 0

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(-1q + -6k)' equal to zero and attempt to solve:

Simplifying
-1q + -6k = 0

Reorder the terms:
-6k + -1q = 0

Solving
-6k + -1q = 0

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

Add 'q' to each side of the equation.
-6k + -1q + q = 0 + q

Combine like terms: -1q + q = 0
-6k + 0 = 0 + q
-6k = 0 + q
Remove the zero:
-6k = q

Divide each side by '-6'.
k = -0.1666666667q

Simplifying
k = -0.1666666667q

Subproblem 3
Set the factor '(q + -2k)' equal to zero and attempt to solve:

Simplifying
q + -2k = 0

Reorder the terms:
-2k + q = 0

Solving
-2k + q = 0

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

Add '-1q' to each side of the equation.
-2k + q + -1q = 0 + -1q

Combine like terms: q + -1q = 0
-2k + 0 = 0 + -1q
-2k = 0 + -1q
Remove the zero:
-2k = -1q

Divide each side by '-2'.
k = 0.5q

Simplifying
k = 0.5q
Solution
k = {-0.1666666667q, 0.5q}

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