36x(5x-20)=185

Solution for 36x(5x-20)=185 equation:

Simplifying
36x(5x + -20) = 185

Reorder the terms:
36x(-20 + 5x) = 185
(-20 * 36x + 5x * 36x) = 185
(-720x + 180x2) = 185

Solving
-720x + 180x2 = 185

Solving for variable 'x'.

Reorder the terms:
-185 + -720x + 180x2 = 185 + -185

Combine like terms: 185 + -185 = 0
-185 + -720x + 180x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-37 + -144x + 36x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-37 + -144x + 36x2)' equal to zero and attempt to solve:

Simplifying
-37 + -144x + 36x2 = 0

Solving
-37 + -144x + 36x2 = 0

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

Divide each side by '36'.
-1.027777778 + -4x + x2 = 0

Move the constant term to the right:

Add '1.027777778' to each side of the equation.
-1.027777778 + -4x + 1.027777778 + x2 = 0 + 1.027777778

Reorder the terms:
-1.027777778 + 1.027777778 + -4x + x2 = 0 + 1.027777778

Combine like terms: -1.027777778 + 1.027777778 = 0.000000000
0.000000000 + -4x + x2 = 0 + 1.027777778
-4x + x2 = 0 + 1.027777778

Combine like terms: 0 + 1.027777778 = 1.027777778
-4x + x2 = 1.027777778

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 1.027777778 + 4

Reorder the terms:
4 + -4x + x2 = 1.027777778 + 4

Combine like terms: 1.027777778 + 4 = 5.027777778
4 + -4x + x2 = 5.027777778

Factor a perfect square on the left side:
(x + -2)(x + -2) = 5.027777778

Calculate the square root of the right side: 2.242270675

Break this problem into two subproblems by setting 
(x + -2) equal to 2.242270675 and -2.242270675.

Subproblem 1
x + -2 = 2.242270675

Simplifying
x + -2 = 2.242270675

Reorder the terms:
-2 + x = 2.242270675

Solving
-2 + x = 2.242270675

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.242270675 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.242270675 + 2
x = 2.242270675 + 2

Combine like terms: 2.242270675 + 2 = 4.242270675
x = 4.242270675

Simplifying
x = 4.242270675

Subproblem 2
x + -2 = -2.242270675

Simplifying
x + -2 = -2.242270675

Reorder the terms:
-2 + x = -2.242270675

Solving
-2 + x = -2.242270675

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.242270675 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.242270675 + 2
x = -2.242270675 + 2

Combine like terms: -2.242270675 + 2 = -0.242270675
x = -0.242270675

Simplifying
x = -0.242270675

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.242270675, -0.242270675}
Solution
x = {4.242270675, -0.242270675}