36=9x(3x-18)

Solution for 36=9x(3x-18) equation:

Simplifying
36 = 9x(3x + -18)

Reorder the terms:
36 = 9x(-18 + 3x)
36 = (-18 * 9x + 3x * 9x)
36 = (-162x + 27x2)

Solving
36 = -162x + 27x2

Solving for variable 'x'.

Reorder the terms:
36 + 162x + -27x2 = -162x + 162x + 27x2 + -27x2

Combine like terms: -162x + 162x = 0
36 + 162x + -27x2 = 0 + 27x2 + -27x2
36 + 162x + -27x2 = 27x2 + -27x2

Combine like terms: 27x2 + -27x2 = 0
36 + 162x + -27x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(4 + 18x + -3x2) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(4 + 18x + -3x2)' equal to zero and attempt to solve:

Simplifying
4 + 18x + -3x2 = 0

Solving
4 + 18x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-1.333333333 + -6x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -6x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -6x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -6x + x2 = 0 + 1.333333333
-6x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-6x + x2 = 1.333333333

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 1.333333333 + 9

Reorder the terms:
9 + -6x + x2 = 1.333333333 + 9

Combine like terms: 1.333333333 + 9 = 10.333333333
9 + -6x + x2 = 10.333333333

Factor a perfect square on the left side:
(x + -3)(x + -3) = 10.333333333

Calculate the square root of the right side: 3.214550254

Break this problem into two subproblems by setting 
(x + -3) equal to 3.214550254 and -3.214550254.

Subproblem 1
x + -3 = 3.214550254

Simplifying
x + -3 = 3.214550254

Reorder the terms:
-3 + x = 3.214550254

Solving
-3 + x = 3.214550254

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 3.214550254 + 3

Combine like terms: -3 + 3 = 0
0 + x = 3.214550254 + 3
x = 3.214550254 + 3

Combine like terms: 3.214550254 + 3 = 6.214550254
x = 6.214550254

Simplifying
x = 6.214550254

Subproblem 2
x + -3 = -3.214550254

Simplifying
x + -3 = -3.214550254

Reorder the terms:
-3 + x = -3.214550254

Solving
-3 + x = -3.214550254

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -3.214550254 + 3

Combine like terms: -3 + 3 = 0
0 + x = -3.214550254 + 3
x = -3.214550254 + 3

Combine like terms: -3.214550254 + 3 = -0.214550254
x = -0.214550254

Simplifying
x = -0.214550254

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.214550254, -0.214550254}
Solution
x = {6.214550254, -0.214550254}