-7(k+9)=9(k-5)14k

Solution for -7(k+9)=9(k-5)14k equation:

Simplifying
-7(k + 9) = 9(k + -5) * 14k

Reorder the terms:
-7(9 + k) = 9(k + -5) * 14k
(9 * -7 + k * -7) = 9(k + -5) * 14k
(-63 + -7k) = 9(k + -5) * 14k

Reorder the terms:
-63 + -7k = 9(-5 + k) * 14k

Reorder the terms for easier multiplication:
-63 + -7k = 9 * 14k(-5 + k)

Multiply 9 * 14
-63 + -7k = 126k(-5 + k)
-63 + -7k = (-5 * 126k + k * 126k)
-63 + -7k = (-630k + 126k2)

Solving
-63 + -7k = -630k + 126k2

Solving for variable 'k'.

Combine like terms: -7k + 630k = 623k
-63 + 623k + -126k2 = -630k + 126k2 + 630k + -126k2

Reorder the terms:
-63 + 623k + -126k2 = -630k + 630k + 126k2 + -126k2

Combine like terms: -630k + 630k = 0
-63 + 623k + -126k2 = 0 + 126k2 + -126k2
-63 + 623k + -126k2 = 126k2 + -126k2

Combine like terms: 126k2 + -126k2 = 0
-63 + 623k + -126k2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-9 + 89k + -18k2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-9 + 89k + -18k2)' equal to zero and attempt to solve:

Simplifying
-9 + 89k + -18k2 = 0

Solving
-9 + 89k + -18k2 = 0

Begin completing the square.  Divide all terms by
-18 the coefficient of the squared term: 

Divide each side by '-18'.
0.5 + -4.944444444k + k2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -4.944444444k + -0.5 + k2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -4.944444444k + k2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -4.944444444k + k2 = 0 + -0.5
-4.944444444k + k2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-4.944444444k + k2 = -0.5

The k term is -4.944444444k.  Take half its coefficient (-2.472222222).
Square it (6.111882715) and add it to both sides.

Add '6.111882715' to each side of the equation.
-4.944444444k + 6.111882715 + k2 = -0.5 + 6.111882715

Reorder the terms:
6.111882715 + -4.944444444k + k2 = -0.5 + 6.111882715

Combine like terms: -0.5 + 6.111882715 = 5.611882715
6.111882715 + -4.944444444k + k2 = 5.611882715

Factor a perfect square on the left side:
(k + -2.472222222)(k + -2.472222222) = 5.611882715

Calculate the square root of the right side: 2.368941265

Break this problem into two subproblems by setting 
(k + -2.472222222) equal to 2.368941265 and -2.368941265.

Subproblem 1
k + -2.472222222 = 2.368941265

Simplifying
k + -2.472222222 = 2.368941265

Reorder the terms:
-2.472222222 + k = 2.368941265

Solving
-2.472222222 + k = 2.368941265

Solving for variable 'k'.

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

Add '2.472222222' to each side of the equation.
-2.472222222 + 2.472222222 + k = 2.368941265 + 2.472222222

Combine like terms: -2.472222222 + 2.472222222 = 0.000000000
0.000000000 + k = 2.368941265 + 2.472222222
k = 2.368941265 + 2.472222222

Combine like terms: 2.368941265 + 2.472222222 = 4.841163487
k = 4.841163487

Simplifying
k = 4.841163487

Subproblem 2
k + -2.472222222 = -2.368941265

Simplifying
k + -2.472222222 = -2.368941265

Reorder the terms:
-2.472222222 + k = -2.368941265

Solving
-2.472222222 + k = -2.368941265

Solving for variable 'k'.

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

Add '2.472222222' to each side of the equation.
-2.472222222 + 2.472222222 + k = -2.368941265 + 2.472222222

Combine like terms: -2.472222222 + 2.472222222 = 0.000000000
0.000000000 + k = -2.368941265 + 2.472222222
k = -2.368941265 + 2.472222222

Combine like terms: -2.368941265 + 2.472222222 = 0.103280957
k = 0.103280957

Simplifying
k = 0.103280957

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {4.841163487, 0.103280957}
Solution
k = {4.841163487, 0.103280957}