3(x-4)-9=2x(x-6)

Solution for 3(x-4)-9=2x(x-6) equation:

Simplifying
3(x + -4) + -9 = 2x(x + -6)

Reorder the terms:
3(-4 + x) + -9 = 2x(x + -6)
(-4 * 3 + x * 3) + -9 = 2x(x + -6)
(-12 + 3x) + -9 = 2x(x + -6)

Reorder the terms:
-12 + -9 + 3x = 2x(x + -6)

Combine like terms: -12 + -9 = -21
-21 + 3x = 2x(x + -6)

Reorder the terms:
-21 + 3x = 2x(-6 + x)
-21 + 3x = (-6 * 2x + x * 2x)
-21 + 3x = (-12x + 2x2)

Solving
-21 + 3x = -12x + 2x2

Solving for variable 'x'.

Combine like terms: 3x + 12x = 15x
-21 + 15x + -2x2 = -12x + 2x2 + 12x + -2x2

Reorder the terms:
-21 + 15x + -2x2 = -12x + 12x + 2x2 + -2x2

Combine like terms: -12x + 12x = 0
-21 + 15x + -2x2 = 0 + 2x2 + -2x2
-21 + 15x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-21 + 15x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
10.5 + -7.5x + x2 = 0

Move the constant term to the right:

Add '-10.5' to each side of the equation.
10.5 + -7.5x + -10.5 + x2 = 0 + -10.5

Reorder the terms:
10.5 + -10.5 + -7.5x + x2 = 0 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + -7.5x + x2 = 0 + -10.5
-7.5x + x2 = 0 + -10.5

Combine like terms: 0 + -10.5 = -10.5
-7.5x + x2 = -10.5

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = -10.5 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = -10.5 + 14.0625

Combine like terms: -10.5 + 14.0625 = 3.5625
14.0625 + -7.5x + x2 = 3.5625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(x + -3.75) equal to 1.887458609 and -1.887458609.

Subproblem 1
x + -3.75 = 1.887458609

Simplifying
x + -3.75 = 1.887458609

Reorder the terms:
-3.75 + x = 1.887458609

Solving
-3.75 + x = 1.887458609

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 1.887458609 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 1.887458609 + 3.75
x = 1.887458609 + 3.75

Combine like terms: 1.887458609 + 3.75 = 5.637458609
x = 5.637458609

Simplifying
x = 5.637458609

Subproblem 2
x + -3.75 = -1.887458609

Simplifying
x + -3.75 = -1.887458609

Reorder the terms:
-3.75 + x = -1.887458609

Solving
-3.75 + x = -1.887458609

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -1.887458609 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -1.887458609 + 3.75
x = -1.887458609 + 3.75

Combine like terms: -1.887458609 + 3.75 = 1.862541391
x = 1.862541391

Simplifying
x = 1.862541391

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.637458609, 1.862541391}