6k(4+3k)+4(-3-8k)=

Solution for 6k(4+3k)+4(-3-8k)= equation:

Simplifying
6k(4 + 3k) + 4(-3 + -8k) = 0
(4 * 6k + 3k * 6k) + 4(-3 + -8k) = 0
(24k + 18k2) + 4(-3 + -8k) = 0
24k + 18k2 + (-3 * 4 + -8k * 4) = 0
24k + 18k2 + (-12 + -32k) = 0

Reorder the terms:
-12 + 24k + -32k + 18k2 = 0

Combine like terms: 24k + -32k = -8k
-12 + -8k + 18k2 = 0

Solving
-12 + -8k + 18k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -4k + 9k2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -4k + 9k2)' equal to zero and attempt to solve:

Simplifying
-6 + -4k + 9k2 = 0

Solving
-6 + -4k + 9k2 = 0

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

Divide each side by '9'.
-0.6666666667 + -0.4444444444k + k2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -0.4444444444k + 0.6666666667 + k2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -0.4444444444k + k2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -0.4444444444k + k2 = 0 + 0.6666666667
-0.4444444444k + k2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-0.4444444444k + k2 = 0.6666666667

The k term is -0.4444444444k.  Take half its coefficient (-0.2222222222).
Square it (0.04938271604) and add it to both sides.

Add '0.04938271604' to each side of the equation.
-0.4444444444k + 0.04938271604 + k2 = 0.6666666667 + 0.04938271604

Reorder the terms:
0.04938271604 + -0.4444444444k + k2 = 0.6666666667 + 0.04938271604

Combine like terms: 0.6666666667 + 0.04938271604 = 0.71604938274
0.04938271604 + -0.4444444444k + k2 = 0.71604938274

Factor a perfect square on the left side:
(k + -0.2222222222)(k + -0.2222222222) = 0.71604938274

Calculate the square root of the right side: 0.846197012

Break this problem into two subproblems by setting 
(k + -0.2222222222) equal to 0.846197012 and -0.846197012.

Subproblem 1
k + -0.2222222222 = 0.846197012

Simplifying
k + -0.2222222222 = 0.846197012

Reorder the terms:
-0.2222222222 + k = 0.846197012

Solving
-0.2222222222 + k = 0.846197012

Solving for variable 'k'.

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

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 0.2222222222 + k = 0.846197012 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + k = 0.846197012 + 0.2222222222
k = 0.846197012 + 0.2222222222

Combine like terms: 0.846197012 + 0.2222222222 = 1.0684192342
k = 1.0684192342

Simplifying
k = 1.0684192342

Subproblem 2
k + -0.2222222222 = -0.846197012

Simplifying
k + -0.2222222222 = -0.846197012

Reorder the terms:
-0.2222222222 + k = -0.846197012

Solving
-0.2222222222 + k = -0.846197012

Solving for variable 'k'.

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

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 0.2222222222 + k = -0.846197012 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + k = -0.846197012 + 0.2222222222
k = -0.846197012 + 0.2222222222

Combine like terms: -0.846197012 + 0.2222222222 = -0.6239747898
k = -0.6239747898

Simplifying
k = -0.6239747898

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.0684192342, -0.6239747898}
Solution
k = {1.0684192342, -0.6239747898}