12k^3=-2k^2+4k

Solution for 12k^3=-2k^2+4k equation:

Simplifying
12k3 = -2k2 + 4k

Reorder the terms:
12k3 = 4k + -2k2

Solving
12k3 = 4k + -2k2

Solving for variable 'k'.

Reorder the terms:
-4k + 2k2 + 12k3 = 4k + -2k2 + -4k + 2k2

Reorder the terms:
-4k + 2k2 + 12k3 = 4k + -4k + -2k2 + 2k2

Combine like terms: 4k + -4k = 0
-4k + 2k2 + 12k3 = 0 + -2k2 + 2k2
-4k + 2k2 + 12k3 = -2k2 + 2k2

Combine like terms: -2k2 + 2k2 = 0
-4k + 2k2 + 12k3 = 0

Factor out the Greatest Common Factor (GCF), '2k'.
2k(-2 + k + 6k2) = 0

Factor a trinomial.
2k((-2 + -3k)(1 + -2k)) = 0

Ignore the factor 2.
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 '(-2 + -3k)' equal to zero and attempt to solve:

Simplifying
-2 + -3k = 0

Solving
-2 + -3k = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3k = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3k = 0 + 2
-3k = 0 + 2

Combine like terms: 0 + 2 = 2
-3k = 2

Divide each side by '-3'.
k = -0.6666666667

Simplifying
k = -0.6666666667
Subproblem 3
Set the factor '(1 + -2k)' equal to zero and attempt to solve:

Simplifying
1 + -2k = 0

Solving
1 + -2k = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -2k = 0 + -1
-2k = 0 + -1

Combine like terms: 0 + -1 = -1
-2k = -1

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

Simplifying
k = 0.5
Solution
k = {0, -0.6666666667, 0.5}