2=4(3k-8)11k

Solution for 2=4(3k-8)11k equation:

Simplifying
2 = 4(3k + -8) * 11k

Reorder the terms:
2 = 4(-8 + 3k) * 11k

Reorder the terms for easier multiplication:
2 = 4 * 11k(-8 + 3k)

Multiply 4 * 11
2 = 44k(-8 + 3k)
2 = (-8 * 44k + 3k * 44k)
2 = (-352k + 132k2)

Solving
2 = -352k + 132k2

Solving for variable 'k'.

Reorder the terms:
2 + 352k + -132k2 = -352k + 352k + 132k2 + -132k2

Combine like terms: -352k + 352k = 0
2 + 352k + -132k2 = 0 + 132k2 + -132k2
2 + 352k + -132k2 = 132k2 + -132k2

Combine like terms: 132k2 + -132k2 = 0
2 + 352k + -132k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 176k + -66k2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + 176k + -66k2)' equal to zero and attempt to solve:

Simplifying
1 + 176k + -66k2 = 0

Solving
1 + 176k + -66k2 = 0

Begin completing the square.  Divide all terms by
-66 the coefficient of the squared term: 

Divide each side by '-66'.
-0.01515151515 + -2.666666667k + k2 = 0

Move the constant term to the right:

Add '0.01515151515' to each side of the equation.
-0.01515151515 + -2.666666667k + 0.01515151515 + k2 = 0 + 0.01515151515

Reorder the terms:
-0.01515151515 + 0.01515151515 + -2.666666667k + k2 = 0 + 0.01515151515

Combine like terms: -0.01515151515 + 0.01515151515 = 0.00000000000
0.00000000000 + -2.666666667k + k2 = 0 + 0.01515151515
-2.666666667k + k2 = 0 + 0.01515151515

Combine like terms: 0 + 0.01515151515 = 0.01515151515
-2.666666667k + k2 = 0.01515151515

The k term is -2.666666667k.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667k + 1.777777780 + k2 = 0.01515151515 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667k + k2 = 0.01515151515 + 1.777777780

Combine like terms: 0.01515151515 + 1.777777780 = 1.79292929515
1.777777780 + -2.666666667k + k2 = 1.79292929515

Factor a perfect square on the left side:
(k + -1.333333334)(k + -1.333333334) = 1.79292929515

Calculate the square root of the right side: 1.339003098

Break this problem into two subproblems by setting 
(k + -1.333333334) equal to 1.339003098 and -1.339003098.

Subproblem 1
k + -1.333333334 = 1.339003098

Simplifying
k + -1.333333334 = 1.339003098

Reorder the terms:
-1.333333334 + k = 1.339003098

Solving
-1.333333334 + k = 1.339003098

Solving for variable 'k'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + k = 1.339003098 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + k = 1.339003098 + 1.333333334
k = 1.339003098 + 1.333333334

Combine like terms: 1.339003098 + 1.333333334 = 2.672336432
k = 2.672336432

Simplifying
k = 2.672336432

Subproblem 2
k + -1.333333334 = -1.339003098

Simplifying
k + -1.333333334 = -1.339003098

Reorder the terms:
-1.333333334 + k = -1.339003098

Solving
-1.333333334 + k = -1.339003098

Solving for variable 'k'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + k = -1.339003098 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + k = -1.339003098 + 1.333333334
k = -1.339003098 + 1.333333334

Combine like terms: -1.339003098 + 1.333333334 = -0.005669764
k = -0.005669764

Simplifying
k = -0.005669764

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2.672336432, -0.005669764}
Solution
k = {2.672336432, -0.005669764}