9k(k-7)=6

Solution for 9k(k-7)=6 equation:

Simplifying
9k(k + -7) = 6

Reorder the terms:
9k(-7 + k) = 6
(-7 * 9k + k * 9k) = 6
(-63k + 9k2) = 6

Solving
-63k + 9k2 = 6

Solving for variable 'k'.

Reorder the terms:
-6 + -63k + 9k2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -63k + 9k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -21k + 3k2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -21k + 3k2)' equal to zero and attempt to solve:

Simplifying
-2 + -21k + 3k2 = 0

Solving
-2 + -21k + 3k2 = 0

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

Divide each side by '3'.
-0.6666666667 + -7k + k2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -7k + 0.6666666667 + k2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -7k + k2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -7k + k2 = 0 + 0.6666666667
-7k + k2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-7k + k2 = 0.6666666667

The k term is -7k.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7k + 12.25 + k2 = 0.6666666667 + 12.25

Reorder the terms:
12.25 + -7k + k2 = 0.6666666667 + 12.25

Combine like terms: 0.6666666667 + 12.25 = 12.9166666667
12.25 + -7k + k2 = 12.9166666667

Factor a perfect square on the left side:
(k + -3.5)(k + -3.5) = 12.9166666667

Calculate the square root of the right side: 3.593976442

Break this problem into two subproblems by setting 
(k + -3.5) equal to 3.593976442 and -3.593976442.

Subproblem 1
k + -3.5 = 3.593976442

Simplifying
k + -3.5 = 3.593976442

Reorder the terms:
-3.5 + k = 3.593976442

Solving
-3.5 + k = 3.593976442

Solving for variable 'k'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + k = 3.593976442 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + k = 3.593976442 + 3.5
k = 3.593976442 + 3.5

Combine like terms: 3.593976442 + 3.5 = 7.093976442
k = 7.093976442

Simplifying
k = 7.093976442

Subproblem 2
k + -3.5 = -3.593976442

Simplifying
k + -3.5 = -3.593976442

Reorder the terms:
-3.5 + k = -3.593976442

Solving
-3.5 + k = -3.593976442

Solving for variable 'k'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + k = -3.593976442 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + k = -3.593976442 + 3.5
k = -3.593976442 + 3.5

Combine like terms: -3.593976442 + 3.5 = -0.093976442
k = -0.093976442

Simplifying
k = -0.093976442

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {7.093976442, -0.093976442}
Solution
k = {7.093976442, -0.093976442}