(400-20x)(12-x)=144

Solution for (400-20x)(12-x)=144 equation:

Simplifying
(400 + -20x)(12 + -1x) = 144

Multiply (400 + -20x) * (12 + -1x)
(400(12 + -1x) + -20x * (12 + -1x)) = 144
((12 * 400 + -1x * 400) + -20x * (12 + -1x)) = 144
((4800 + -400x) + -20x * (12 + -1x)) = 144
(4800 + -400x + (12 * -20x + -1x * -20x)) = 144
(4800 + -400x + (-240x + 20x2)) = 144

Combine like terms: -400x + -240x = -640x
(4800 + -640x + 20x2) = 144

Solving
4800 + -640x + 20x2 = 144

Solving for variable 'x'.

Reorder the terms:
4800 + -144 + -640x + 20x2 = 144 + -144

Combine like terms: 4800 + -144 = 4656
4656 + -640x + 20x2 = 144 + -144

Combine like terms: 144 + -144 = 0
4656 + -640x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1164 + -160x + 5x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1164 + -160x + 5x2)' equal to zero and attempt to solve:

Simplifying
1164 + -160x + 5x2 = 0

Solving
1164 + -160x + 5x2 = 0

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

Divide each side by '5'.
232.8 + -32x + x2 = 0

Move the constant term to the right:

Add '-232.8' to each side of the equation.
232.8 + -32x + -232.8 + x2 = 0 + -232.8

Reorder the terms:
232.8 + -232.8 + -32x + x2 = 0 + -232.8

Combine like terms: 232.8 + -232.8 = 0.0
0.0 + -32x + x2 = 0 + -232.8
-32x + x2 = 0 + -232.8

Combine like terms: 0 + -232.8 = -232.8
-32x + x2 = -232.8

The x term is -32x.  Take half its coefficient (-16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
-32x + 256 + x2 = -232.8 + 256

Reorder the terms:
256 + -32x + x2 = -232.8 + 256

Combine like terms: -232.8 + 256 = 23.2
256 + -32x + x2 = 23.2

Factor a perfect square on the left side:
(x + -16)(x + -16) = 23.2

Calculate the square root of the right side: 4.816637832

Break this problem into two subproblems by setting 
(x + -16) equal to 4.816637832 and -4.816637832.

Subproblem 1
x + -16 = 4.816637832

Simplifying
x + -16 = 4.816637832

Reorder the terms:
-16 + x = 4.816637832

Solving
-16 + x = 4.816637832

Solving for variable 'x'.

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

Add '16' to each side of the equation.
-16 + 16 + x = 4.816637832 + 16

Combine like terms: -16 + 16 = 0
0 + x = 4.816637832 + 16
x = 4.816637832 + 16

Combine like terms: 4.816637832 + 16 = 20.816637832
x = 20.816637832

Simplifying
x = 20.816637832

Subproblem 2
x + -16 = -4.816637832

Simplifying
x + -16 = -4.816637832

Reorder the terms:
-16 + x = -4.816637832

Solving
-16 + x = -4.816637832

Solving for variable 'x'.

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

Add '16' to each side of the equation.
-16 + 16 + x = -4.816637832 + 16

Combine like terms: -16 + 16 = 0
0 + x = -4.816637832 + 16
x = -4.816637832 + 16

Combine like terms: -4.816637832 + 16 = 11.183362168
x = 11.183362168

Simplifying
x = 11.183362168

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.816637832, 11.183362168}
Solution
x = {20.816637832, 11.183362168}