3x-9=3x(12-x)

Solution for 3x-9=3x(12-x) equation:

Simplifying
3x + -9 = 3x(12 + -1x)

Reorder the terms:
-9 + 3x = 3x(12 + -1x)
-9 + 3x = (12 * 3x + -1x * 3x)
-9 + 3x = (36x + -3x2)

Solving
-9 + 3x = 36x + -3x2

Solving for variable 'x'.

Combine like terms: 3x + -36x = -33x
-9 + -33x + 3x2 = 36x + -3x2 + -36x + 3x2

Reorder the terms:
-9 + -33x + 3x2 = 36x + -36x + -3x2 + 3x2

Combine like terms: 36x + -36x = 0
-9 + -33x + 3x2 = 0 + -3x2 + 3x2
-9 + -33x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-9 + -33x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -11x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + -11x + x2)' equal to zero and attempt to solve:

Simplifying
-3 + -11x + x2 = 0

Solving
-3 + -11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -11x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -11x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -11x + x2 = 0 + 3
-11x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-11x + x2 = 3

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = 3 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 3 + 30.25

Combine like terms: 3 + 30.25 = 33.25
30.25 + -11x + x2 = 33.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 33.25

Calculate the square root of the right side: 5.766281297

Break this problem into two subproblems by setting 
(x + -5.5) equal to 5.766281297 and -5.766281297.

Subproblem 1
x + -5.5 = 5.766281297

Simplifying
x + -5.5 = 5.766281297

Reorder the terms:
-5.5 + x = 5.766281297

Solving
-5.5 + x = 5.766281297

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 5.766281297 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 5.766281297 + 5.5
x = 5.766281297 + 5.5

Combine like terms: 5.766281297 + 5.5 = 11.266281297
x = 11.266281297

Simplifying
x = 11.266281297

Subproblem 2
x + -5.5 = -5.766281297

Simplifying
x + -5.5 = -5.766281297

Reorder the terms:
-5.5 + x = -5.766281297

Solving
-5.5 + x = -5.766281297

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -5.766281297 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -5.766281297 + 5.5
x = -5.766281297 + 5.5

Combine like terms: -5.766281297 + 5.5 = -0.266281297
x = -0.266281297

Simplifying
x = -0.266281297

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.266281297, -0.266281297}
Solution
x = {11.266281297, -0.266281297}