3x+6x(x-9)=3(x-12)

Solution for 3x+6x(x-9)=3(x-12) equation:

Simplifying
3x + 6x(x + -9) = 3(x + -12)

Reorder the terms:
3x + 6x(-9 + x) = 3(x + -12)
3x + (-9 * 6x + x * 6x) = 3(x + -12)
3x + (-54x + 6x2) = 3(x + -12)

Combine like terms: 3x + -54x = -51x
-51x + 6x2 = 3(x + -12)

Reorder the terms:
-51x + 6x2 = 3(-12 + x)
-51x + 6x2 = (-12 * 3 + x * 3)
-51x + 6x2 = (-36 + 3x)

Solving
-51x + 6x2 = -36 + 3x

Solving for variable 'x'.

Reorder the terms:
36 + -51x + -3x + 6x2 = -36 + 3x + 36 + -3x

Combine like terms: -51x + -3x = -54x
36 + -54x + 6x2 = -36 + 3x + 36 + -3x

Reorder the terms:
36 + -54x + 6x2 = -36 + 36 + 3x + -3x

Combine like terms: -36 + 36 = 0
36 + -54x + 6x2 = 0 + 3x + -3x
36 + -54x + 6x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
36 + -54x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(6 + -9x + x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(6 + -9x + x2)' equal to zero and attempt to solve:

Simplifying
6 + -9x + x2 = 0

Solving
6 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -9x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -9x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -9x + x2 = 0 + -6
-9x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-9x + x2 = -6

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -6 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -6 + 20.25

Combine like terms: -6 + 20.25 = 14.25
20.25 + -9x + x2 = 14.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + -4.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
x + -4.5 = 3.774917218

Simplifying
x + -4.5 = 3.774917218

Reorder the terms:
-4.5 + x = 3.774917218

Solving
-4.5 + x = 3.774917218

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 3.774917218 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 3.774917218 + 4.5
x = 3.774917218 + 4.5

Combine like terms: 3.774917218 + 4.5 = 8.274917218
x = 8.274917218

Simplifying
x = 8.274917218

Subproblem 2
x + -4.5 = -3.774917218

Simplifying
x + -4.5 = -3.774917218

Reorder the terms:
-4.5 + x = -3.774917218

Solving
-4.5 + x = -3.774917218

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -3.774917218 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -3.774917218 + 4.5
x = -3.774917218 + 4.5

Combine like terms: -3.774917218 + 4.5 = 0.725082782
x = 0.725082782

Simplifying
x = 0.725082782

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.274917218, 0.725082782}
Solution
x = {8.274917218, 0.725082782}