1.3(k-6)(k-6)=20

Solution for 1.3(k-6)(k-6)=20 equation:

Simplifying
1.3(k + -6)(k + -6) = 20

Reorder the terms:
1.3(-6 + k)(k + -6) = 20

Reorder the terms:
1.3(-6 + k)(-6 + k) = 20

Multiply (-6 + k) * (-6 + k)
1.3(-6(-6 + k) + k(-6 + k)) = 20
1.3((-6 * -6 + k * -6) + k(-6 + k)) = 20
1.3((36 + -6k) + k(-6 + k)) = 20
1.3(36 + -6k + (-6 * k + k * k)) = 20
1.3(36 + -6k + (-6k + k2)) = 20

Combine like terms: -6k + -6k = -12k
1.3(36 + -12k + k2) = 20
(36 * 1.3 + -12k * 1.3 + k2 * 1.3) = 20
(46.8 + -15.6k + 1.3k2) = 20

Solving
46.8 + -15.6k + 1.3k2 = 20

Solving for variable 'k'.

Reorder the terms:
46.8 + -20 + -15.6k + 1.3k2 = 20 + -20

Combine like terms: 46.8 + -20 = 26.8
26.8 + -15.6k + 1.3k2 = 20 + -20

Combine like terms: 20 + -20 = 0
26.8 + -15.6k + 1.3k2 = 0

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

Divide each side by '1.3'.
20.61538462 + -12k + k2 = 0

Move the constant term to the right:

Add '-20.61538462' to each side of the equation.
20.61538462 + -12k + -20.61538462 + k2 = 0 + -20.61538462

Reorder the terms:
20.61538462 + -20.61538462 + -12k + k2 = 0 + -20.61538462

Combine like terms: 20.61538462 + -20.61538462 = 0.00000000
0.00000000 + -12k + k2 = 0 + -20.61538462
-12k + k2 = 0 + -20.61538462

Combine like terms: 0 + -20.61538462 = -20.61538462
-12k + k2 = -20.61538462

The k term is -12k.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12k + 36 + k2 = -20.61538462 + 36

Reorder the terms:
36 + -12k + k2 = -20.61538462 + 36

Combine like terms: -20.61538462 + 36 = 15.38461538
36 + -12k + k2 = 15.38461538

Factor a perfect square on the left side:
(k + -6)(k + -6) = 15.38461538

Calculate the square root of the right side: 3.922322702

Break this problem into two subproblems by setting 
(k + -6) equal to 3.922322702 and -3.922322702.

Subproblem 1
k + -6 = 3.922322702

Simplifying
k + -6 = 3.922322702

Reorder the terms:
-6 + k = 3.922322702

Solving
-6 + k = 3.922322702

Solving for variable 'k'.

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

Add '6' to each side of the equation.
-6 + 6 + k = 3.922322702 + 6

Combine like terms: -6 + 6 = 0
0 + k = 3.922322702 + 6
k = 3.922322702 + 6

Combine like terms: 3.922322702 + 6 = 9.922322702
k = 9.922322702

Simplifying
k = 9.922322702

Subproblem 2
k + -6 = -3.922322702

Simplifying
k + -6 = -3.922322702

Reorder the terms:
-6 + k = -3.922322702

Solving
-6 + k = -3.922322702

Solving for variable 'k'.

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

Add '6' to each side of the equation.
-6 + 6 + k = -3.922322702 + 6

Combine like terms: -6 + 6 = 0
0 + k = -3.922322702 + 6
k = -3.922322702 + 6

Combine like terms: -3.922322702 + 6 = 2.077677298
k = 2.077677298

Simplifying
k = 2.077677298

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {9.922322702, 2.077677298}