73=6(k-7)6k+5

Solution for 73=6(k-7)6k+5 equation:

Simplifying
73 = 6(k + -7) * 6k + 5

Reorder the terms:
73 = 6(-7 + k) * 6k + 5

Reorder the terms for easier multiplication:
73 = 6 * 6k(-7 + k) + 5

Multiply 6 * 6
73 = 36k(-7 + k) + 5
73 = (-7 * 36k + k * 36k) + 5
73 = (-252k + 36k2) + 5

Reorder the terms:
73 = 5 + -252k + 36k2

Solving
73 = 5 + -252k + 36k2

Solving for variable 'k'.

Combine like terms: 73 + -5 = 68
68 + 252k + -36k2 = 5 + -252k + 36k2 + -5 + 252k + -36k2

Reorder the terms:
68 + 252k + -36k2 = 5 + -5 + -252k + 252k + 36k2 + -36k2

Combine like terms: 5 + -5 = 0
68 + 252k + -36k2 = 0 + -252k + 252k + 36k2 + -36k2
68 + 252k + -36k2 = -252k + 252k + 36k2 + -36k2

Combine like terms: -252k + 252k = 0
68 + 252k + -36k2 = 0 + 36k2 + -36k2
68 + 252k + -36k2 = 36k2 + -36k2

Combine like terms: 36k2 + -36k2 = 0
68 + 252k + -36k2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(17 + 63k + -9k2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(17 + 63k + -9k2)' equal to zero and attempt to solve:

Simplifying
17 + 63k + -9k2 = 0

Solving
17 + 63k + -9k2 = 0

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

Divide each side by '-9'.
-1.888888889 + -7k + k2 = 0

Move the constant term to the right:

Add '1.888888889' to each side of the equation.
-1.888888889 + -7k + 1.888888889 + k2 = 0 + 1.888888889

Reorder the terms:
-1.888888889 + 1.888888889 + -7k + k2 = 0 + 1.888888889

Combine like terms: -1.888888889 + 1.888888889 = 0.000000000
0.000000000 + -7k + k2 = 0 + 1.888888889
-7k + k2 = 0 + 1.888888889

Combine like terms: 0 + 1.888888889 = 1.888888889
-7k + k2 = 1.888888889

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 = 1.888888889 + 12.25

Reorder the terms:
12.25 + -7k + k2 = 1.888888889 + 12.25

Combine like terms: 1.888888889 + 12.25 = 14.138888889
12.25 + -7k + k2 = 14.138888889

Factor a perfect square on the left side:
(k + -3.5)(k + -3.5) = 14.138888889

Calculate the square root of the right side: 3.760171391

Break this problem into two subproblems by setting 
(k + -3.5) equal to 3.760171391 and -3.760171391.

Subproblem 1
k + -3.5 = 3.760171391

Simplifying
k + -3.5 = 3.760171391

Reorder the terms:
-3.5 + k = 3.760171391

Solving
-3.5 + k = 3.760171391

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 = 3.760171391 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + k = 3.760171391 + 3.5
k = 3.760171391 + 3.5

Combine like terms: 3.760171391 + 3.5 = 7.260171391
k = 7.260171391

Simplifying
k = 7.260171391

Subproblem 2
k + -3.5 = -3.760171391

Simplifying
k + -3.5 = -3.760171391

Reorder the terms:
-3.5 + k = -3.760171391

Solving
-3.5 + k = -3.760171391

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 = -3.760171391 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + k = -3.760171391 + 3.5
k = -3.760171391 + 3.5

Combine like terms: -3.760171391 + 3.5 = -0.260171391
k = -0.260171391

Simplifying
k = -0.260171391

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {7.260171391, -0.260171391}
Solution
k = {7.260171391, -0.260171391}