5k^2(6k^2-2k+6)=

Solution for 5k^2(6k^2-2k+6)= equation:

Simplifying
5k2(6k2 + -2k + 6) = 0

Reorder the terms:
5k2(6 + -2k + 6k2) = 0
(6 * 5k2 + -2k * 5k2 + 6k2 * 5k2) = 0
(30k2 + -10k3 + 30k4) = 0

Solving
30k2 + -10k3 + 30k4 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '10k2'.
10k2(3 + -1k + 3k2) = 0

Ignore the factor 10.
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 = -0.97222222221
0.02777777779 + -0.3333333333k + k2 = -0.97222222221

Factor a perfect square on the left side:
(k + -0.1666666667)(k + -0.1666666667) = -0.97222222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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