9(k-4)7k=32-2(k+8)

Solution for 9(k-4)7k=32-2(k+8) equation:

Simplifying
9(k + -4) * 7k = 32 + -2(k + 8)

Reorder the terms:
9(-4 + k) * 7k = 32 + -2(k + 8)

Reorder the terms for easier multiplication:
9 * 7k(-4 + k) = 32 + -2(k + 8)

Multiply 9 * 7
63k(-4 + k) = 32 + -2(k + 8)
(-4 * 63k + k * 63k) = 32 + -2(k + 8)
(-252k + 63k2) = 32 + -2(k + 8)

Reorder the terms:
-252k + 63k2 = 32 + -2(8 + k)
-252k + 63k2 = 32 + (8 * -2 + k * -2)
-252k + 63k2 = 32 + (-16 + -2k)

Combine like terms: 32 + -16 = 16
-252k + 63k2 = 16 + -2k

Solving
-252k + 63k2 = 16 + -2k

Solving for variable 'k'.

Reorder the terms:
-16 + -252k + 2k + 63k2 = 16 + -2k + -16 + 2k

Combine like terms: -252k + 2k = -250k
-16 + -250k + 63k2 = 16 + -2k + -16 + 2k

Reorder the terms:
-16 + -250k + 63k2 = 16 + -16 + -2k + 2k

Combine like terms: 16 + -16 = 0
-16 + -250k + 63k2 = 0 + -2k + 2k
-16 + -250k + 63k2 = -2k + 2k

Combine like terms: -2k + 2k = 0
-16 + -250k + 63k2 = 0

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

Divide each side by '63'.
-0.253968254 + -3.968253968k + k2 = 0

Move the constant term to the right:

Add '0.253968254' to each side of the equation.
-0.253968254 + -3.968253968k + 0.253968254 + k2 = 0 + 0.253968254

Reorder the terms:
-0.253968254 + 0.253968254 + -3.968253968k + k2 = 0 + 0.253968254

Combine like terms: -0.253968254 + 0.253968254 = 0.000000000
0.000000000 + -3.968253968k + k2 = 0 + 0.253968254
-3.968253968k + k2 = 0 + 0.253968254

Combine like terms: 0 + 0.253968254 = 0.253968254
-3.968253968k + k2 = 0.253968254

The k term is -3.968253968k.  Take half its coefficient (-1.984126984).
Square it (3.936759889) and add it to both sides.

Add '3.936759889' to each side of the equation.
-3.968253968k + 3.936759889 + k2 = 0.253968254 + 3.936759889

Reorder the terms:
3.936759889 + -3.968253968k + k2 = 0.253968254 + 3.936759889

Combine like terms: 0.253968254 + 3.936759889 = 4.190728143
3.936759889 + -3.968253968k + k2 = 4.190728143

Factor a perfect square on the left side:
(k + -1.984126984)(k + -1.984126984) = 4.190728143

Calculate the square root of the right side: 2.047126802

Break this problem into two subproblems by setting 
(k + -1.984126984) equal to 2.047126802 and -2.047126802.

Subproblem 1
k + -1.984126984 = 2.047126802

Simplifying
k + -1.984126984 = 2.047126802

Reorder the terms:
-1.984126984 + k = 2.047126802

Solving
-1.984126984 + k = 2.047126802

Solving for variable 'k'.

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

Add '1.984126984' to each side of the equation.
-1.984126984 + 1.984126984 + k = 2.047126802 + 1.984126984

Combine like terms: -1.984126984 + 1.984126984 = 0.000000000
0.000000000 + k = 2.047126802 + 1.984126984
k = 2.047126802 + 1.984126984

Combine like terms: 2.047126802 + 1.984126984 = 4.031253786
k = 4.031253786

Simplifying
k = 4.031253786

Subproblem 2
k + -1.984126984 = -2.047126802

Simplifying
k + -1.984126984 = -2.047126802

Reorder the terms:
-1.984126984 + k = -2.047126802

Solving
-1.984126984 + k = -2.047126802

Solving for variable 'k'.

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

Add '1.984126984' to each side of the equation.
-1.984126984 + 1.984126984 + k = -2.047126802 + 1.984126984

Combine like terms: -1.984126984 + 1.984126984 = 0.000000000
0.000000000 + k = -2.047126802 + 1.984126984
k = -2.047126802 + 1.984126984

Combine like terms: -2.047126802 + 1.984126984 = -0.062999818
k = -0.062999818

Simplifying
k = -0.062999818

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {4.031253786, -0.062999818}