(72-x)(4x+32)=116

Solution for (72-x)(4x+32)=116 equation:

Simplifying
(72 + -1x)(4x + 32) = 116

Reorder the terms:
(72 + -1x)(32 + 4x) = 116

Multiply (72 + -1x) * (32 + 4x)
(72(32 + 4x) + -1x * (32 + 4x)) = 116
((32 * 72 + 4x * 72) + -1x * (32 + 4x)) = 116
((2304 + 288x) + -1x * (32 + 4x)) = 116
(2304 + 288x + (32 * -1x + 4x * -1x)) = 116
(2304 + 288x + (-32x + -4x2)) = 116

Combine like terms: 288x + -32x = 256x
(2304 + 256x + -4x2) = 116

Solving
2304 + 256x + -4x2 = 116

Solving for variable 'x'.

Reorder the terms:
2304 + -116 + 256x + -4x2 = 116 + -116

Combine like terms: 2304 + -116 = 2188
2188 + 256x + -4x2 = 116 + -116

Combine like terms: 116 + -116 = 0
2188 + 256x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(547 + 64x + -1x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(547 + 64x + -1x2)' equal to zero and attempt to solve:

Simplifying
547 + 64x + -1x2 = 0

Solving
547 + 64x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-547 + -64x + x2 = 0

Move the constant term to the right:

Add '547' to each side of the equation.
-547 + -64x + 547 + x2 = 0 + 547

Reorder the terms:
-547 + 547 + -64x + x2 = 0 + 547

Combine like terms: -547 + 547 = 0
0 + -64x + x2 = 0 + 547
-64x + x2 = 0 + 547

Combine like terms: 0 + 547 = 547
-64x + x2 = 547

The x term is -64x.  Take half its coefficient (-32).
Square it (1024) and add it to both sides.

Add '1024' to each side of the equation.
-64x + 1024 + x2 = 547 + 1024

Reorder the terms:
1024 + -64x + x2 = 547 + 1024

Combine like terms: 547 + 1024 = 1571
1024 + -64x + x2 = 1571

Factor a perfect square on the left side:
(x + -32)(x + -32) = 1571

Calculate the square root of the right side: 39.635842365

Break this problem into two subproblems by setting 
(x + -32) equal to 39.635842365 and -39.635842365.

Subproblem 1
x + -32 = 39.635842365

Simplifying
x + -32 = 39.635842365

Reorder the terms:
-32 + x = 39.635842365

Solving
-32 + x = 39.635842365

Solving for variable 'x'.

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

Add '32' to each side of the equation.
-32 + 32 + x = 39.635842365 + 32

Combine like terms: -32 + 32 = 0
0 + x = 39.635842365 + 32
x = 39.635842365 + 32

Combine like terms: 39.635842365 + 32 = 71.635842365
x = 71.635842365

Simplifying
x = 71.635842365

Subproblem 2
x + -32 = -39.635842365

Simplifying
x + -32 = -39.635842365

Reorder the terms:
-32 + x = -39.635842365

Solving
-32 + x = -39.635842365

Solving for variable 'x'.

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

Add '32' to each side of the equation.
-32 + 32 + x = -39.635842365 + 32

Combine like terms: -32 + 32 = 0
0 + x = -39.635842365 + 32
x = -39.635842365 + 32

Combine like terms: -39.635842365 + 32 = -7.635842365
x = -7.635842365

Simplifying
x = -7.635842365

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {71.635842365, -7.635842365}
Solution
x = {71.635842365, -7.635842365}