(x-4)-x+9(x-4)=(x-4)(6x)

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

Simplifying
(x + -4) + -1x + 9(x + -4) = (x + -4)(6x)

Reorder the terms:
(-4 + x) + -1x + 9(x + -4) = (x + -4)(6x)

Remove parenthesis around (-4 + x)
-4 + x + -1x + 9(x + -4) = (x + -4)(6x)

Reorder the terms:
-4 + x + -1x + 9(-4 + x) = (x + -4)(6x)
-4 + x + -1x + (-4 * 9 + x * 9) = (x + -4)(6x)
-4 + x + -1x + (-36 + 9x) = (x + -4)(6x)

Reorder the terms:
-4 + -36 + x + -1x + 9x = (x + -4)(6x)

Combine like terms: -4 + -36 = -40
-40 + x + -1x + 9x = (x + -4)(6x)

Combine like terms: x + -1x = 0
-40 + 0 + 9x = (x + -4)(6x)
-40 + 9x = (x + -4)(6x)

Reorder the terms:
-40 + 9x = (-4 + x)(6x)

Remove parenthesis around (6x)
-40 + 9x = (-4 + x) * 6x

Reorder the terms for easier multiplication:
-40 + 9x = 6x(-4 + x)
-40 + 9x = (-4 * 6x + x * 6x)
-40 + 9x = (-24x + 6x2)

Solving
-40 + 9x = -24x + 6x2

Solving for variable 'x'.

Combine like terms: 9x + 24x = 33x
-40 + 33x + -6x2 = -24x + 6x2 + 24x + -6x2

Reorder the terms:
-40 + 33x + -6x2 = -24x + 24x + 6x2 + -6x2

Combine like terms: -24x + 24x = 0
-40 + 33x + -6x2 = 0 + 6x2 + -6x2
-40 + 33x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-40 + 33x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
6.666666667 + -5.5x + x2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + -5.5x + -6.666666667 + x2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + -5.5x + x2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + -5.5x + x2 = 0 + -6.666666667
-5.5x + x2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
-5.5x + x2 = -6.666666667

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = -6.666666667 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = -6.666666667 + 7.5625

Combine like terms: -6.666666667 + 7.5625 = 0.895833333
7.5625 + -5.5x + x2 = 0.895833333

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 0.895833333

Calculate the square root of the right side: 0.946484724

Break this problem into two subproblems by setting 
(x + -2.75) equal to 0.946484724 and -0.946484724.

Subproblem 1
x + -2.75 = 0.946484724

Simplifying
x + -2.75 = 0.946484724

Reorder the terms:
-2.75 + x = 0.946484724

Solving
-2.75 + x = 0.946484724

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 0.946484724 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 0.946484724 + 2.75
x = 0.946484724 + 2.75

Combine like terms: 0.946484724 + 2.75 = 3.696484724
x = 3.696484724

Simplifying
x = 3.696484724

Subproblem 2
x + -2.75 = -0.946484724

Simplifying
x + -2.75 = -0.946484724

Reorder the terms:
-2.75 + x = -0.946484724

Solving
-2.75 + x = -0.946484724

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -0.946484724 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -0.946484724 + 2.75
x = -0.946484724 + 2.75

Combine like terms: -0.946484724 + 2.75 = 1.803515276
x = 1.803515276

Simplifying
x = 1.803515276

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.696484724, 1.803515276}