2x(x+36)-x(x+47)=75

Solution for 2x(x+36)-x(x+47)=75 equation:

Simplifying
2x(x + 36) + -1x(x + 47) = 75

Reorder the terms:
2x(36 + x) + -1x(x + 47) = 75
(36 * 2x + x * 2x) + -1x(x + 47) = 75
(72x + 2x2) + -1x(x + 47) = 75

Reorder the terms:
72x + 2x2 + -1x(47 + x) = 75
72x + 2x2 + (47 * -1x + x * -1x) = 75
72x + 2x2 + (-47x + -1x2) = 75

Reorder the terms:
72x + -47x + 2x2 + -1x2 = 75

Combine like terms: 72x + -47x = 25x
25x + 2x2 + -1x2 = 75

Combine like terms: 2x2 + -1x2 = 1x2
25x + 1x2 = 75

Solving
25x + 1x2 = 75

Solving for variable 'x'.

Reorder the terms:
-75 + 25x + 1x2 = 75 + -75

Combine like terms: 75 + -75 = 0
-75 + 25x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + 25x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + 25x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + 25x + x2 = 0 + 75
25x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
25x + x2 = 75

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 75 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 75 + 156.25

Combine like terms: 75 + 156.25 = 231.25
156.25 + 25x + x2 = 231.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 231.25

Calculate the square root of the right side: 15.206906326

Break this problem into two subproblems by setting 
(x + 12.5) equal to 15.206906326 and -15.206906326.

Subproblem 1
x + 12.5 = 15.206906326

Simplifying
x + 12.5 = 15.206906326

Reorder the terms:
12.5 + x = 15.206906326

Solving
12.5 + x = 15.206906326

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 15.206906326 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 15.206906326 + -12.5
x = 15.206906326 + -12.5

Combine like terms: 15.206906326 + -12.5 = 2.706906326
x = 2.706906326

Simplifying
x = 2.706906326

Subproblem 2
x + 12.5 = -15.206906326

Simplifying
x + 12.5 = -15.206906326

Reorder the terms:
12.5 + x = -15.206906326

Solving
12.5 + x = -15.206906326

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -15.206906326 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -15.206906326 + -12.5
x = -15.206906326 + -12.5

Combine like terms: -15.206906326 + -12.5 = -27.706906326
x = -27.706906326

Simplifying
x = -27.706906326

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.706906326, -27.706906326}