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

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

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

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

Solving
6k2 + -2k3 + -6k4 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2k2'.
2k2(3 + -1k + -3k2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'k2' equal to zero and attempt to solve:

Simplifying
k2 = 0

Solving
k2 = 0

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

Simplifying
k2 = 0

Take the square root of each side:
k = {0}
Subproblem 2
Set the factor '(3 + -1k + -3k2)' equal to zero and attempt to solve:

Simplifying
3 + -1k + -3k2 = 0

Solving
3 + -1k + -3k2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-1 + 0.3333333333k + k2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.3333333333k + 1 + k2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.3333333333k + k2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.3333333333k + k2 = 0 + 1
0.3333333333k + k2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.3333333333k + k2 = 1

The k term is 0.3333333333k.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333k + 0.02777777779 + k2 = 1 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333k + k2 = 1 + 0.02777777779

Combine like terms: 1 + 0.02777777779 = 1.02777777779
0.02777777779 + 0.3333333333k + k2 = 1.02777777779

Factor a perfect square on the left side:
(k + 0.1666666667)(k + 0.1666666667) = 1.02777777779

Calculate the square root of the right side: 1.013793755

Break this problem into two subproblems by setting 
(k + 0.1666666667) equal to 1.013793755 and -1.013793755.

Subproblem 1
k + 0.1666666667 = 1.013793755

Simplifying
k + 0.1666666667 = 1.013793755

Reorder the terms:
0.1666666667 + k = 1.013793755

Solving
0.1666666667 + k = 1.013793755

Solving for variable 'k'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + k = 1.013793755 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + k = 1.013793755 + -0.1666666667
k = 1.013793755 + -0.1666666667

Combine like terms: 1.013793755 + -0.1666666667 = 0.8471270883
k = 0.8471270883

Simplifying
k = 0.8471270883

Subproblem 2
k + 0.1666666667 = -1.013793755

Simplifying
k + 0.1666666667 = -1.013793755

Reorder the terms:
0.1666666667 + k = -1.013793755

Solving
0.1666666667 + k = -1.013793755

Solving for variable 'k'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + k = -1.013793755 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + k = -1.013793755 + -0.1666666667
k = -1.013793755 + -0.1666666667

Combine like terms: -1.013793755 + -0.1666666667 = -1.1804604217
k = -1.1804604217

Simplifying
k = -1.1804604217

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.8471270883, -1.1804604217}
Solution
k = {0, 0.8471270883, -1.1804604217}