12.8=(104+28x)(20+x)

Solution for 12.8=(104+28x)(20+x) equation:

Simplifying
12.8 = (104 + 28x)(20 + x)

Multiply (104 + 28x) * (20 + x)
12.8 = (104(20 + x) + 28x * (20 + x))
12.8 = ((20 * 104 + x * 104) + 28x * (20 + x))
12.8 = ((2080 + 104x) + 28x * (20 + x))
12.8 = (2080 + 104x + (20 * 28x + x * 28x))
12.8 = (2080 + 104x + (560x + 28x2))

Combine like terms: 104x + 560x = 664x
12.8 = (2080 + 664x + 28x2)

Solving
12.8 = 2080 + 664x + 28x2

Solving for variable 'x'.

Combine like terms: 12.8 + -2080 = -2067.2
-2067.2 + -664x + -28x2 = 2080 + 664x + 28x2 + -2080 + -664x + -28x2

Reorder the terms:
-2067.2 + -664x + -28x2 = 2080 + -2080 + 664x + -664x + 28x2 + -28x2

Combine like terms: 2080 + -2080 = 0
-2067.2 + -664x + -28x2 = 0 + 664x + -664x + 28x2 + -28x2
-2067.2 + -664x + -28x2 = 664x + -664x + 28x2 + -28x2

Combine like terms: 664x + -664x = 0
-2067.2 + -664x + -28x2 = 0 + 28x2 + -28x2
-2067.2 + -664x + -28x2 = 28x2 + -28x2

Combine like terms: 28x2 + -28x2 = 0
-2067.2 + -664x + -28x2 = 0

Begin completing the square.  Divide all terms by
-28 the coefficient of the squared term: 

Divide each side by '-28'.
73.82857143 + 23.71428571x + x2 = 0

Move the constant term to the right:

Add '-73.82857143' to each side of the equation.
73.82857143 + 23.71428571x + -73.82857143 + x2 = 0 + -73.82857143

Reorder the terms:
73.82857143 + -73.82857143 + 23.71428571x + x2 = 0 + -73.82857143

Combine like terms: 73.82857143 + -73.82857143 = 0.00000000
0.00000000 + 23.71428571x + x2 = 0 + -73.82857143
23.71428571x + x2 = 0 + -73.82857143

Combine like terms: 0 + -73.82857143 = -73.82857143
23.71428571x + x2 = -73.82857143

The x term is 23.71428571x.  Take half its coefficient (11.85714286).
Square it (140.5918368) and add it to both sides.

Add '140.5918368' to each side of the equation.
23.71428571x + 140.5918368 + x2 = -73.82857143 + 140.5918368

Reorder the terms:
140.5918368 + 23.71428571x + x2 = -73.82857143 + 140.5918368

Combine like terms: -73.82857143 + 140.5918368 = 66.76326537
140.5918368 + 23.71428571x + x2 = 66.76326537

Factor a perfect square on the left side:
(x + 11.85714286)(x + 11.85714286) = 66.76326537

Calculate the square root of the right side: 8.170879106

Break this problem into two subproblems by setting 
(x + 11.85714286) equal to 8.170879106 and -8.170879106.

Subproblem 1
x + 11.85714286 = 8.170879106

Simplifying
x + 11.85714286 = 8.170879106

Reorder the terms:
11.85714286 + x = 8.170879106

Solving
11.85714286 + x = 8.170879106

Solving for variable 'x'.

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

Add '-11.85714286' to each side of the equation.
11.85714286 + -11.85714286 + x = 8.170879106 + -11.85714286

Combine like terms: 11.85714286 + -11.85714286 = 0.00000000
0.00000000 + x = 8.170879106 + -11.85714286
x = 8.170879106 + -11.85714286

Combine like terms: 8.170879106 + -11.85714286 = -3.686263754
x = -3.686263754

Simplifying
x = -3.686263754

Subproblem 2
x + 11.85714286 = -8.170879106

Simplifying
x + 11.85714286 = -8.170879106

Reorder the terms:
11.85714286 + x = -8.170879106

Solving
11.85714286 + x = -8.170879106

Solving for variable 'x'.

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

Add '-11.85714286' to each side of the equation.
11.85714286 + -11.85714286 + x = -8.170879106 + -11.85714286

Combine like terms: 11.85714286 + -11.85714286 = 0.00000000
0.00000000 + x = -8.170879106 + -11.85714286
x = -8.170879106 + -11.85714286

Combine like terms: -8.170879106 + -11.85714286 = -20.028021966
x = -20.028021966

Simplifying
x = -20.028021966

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.686263754, -20.028021966}