4-9x=6-6x(2(13)+3x)

Solution for 4-9x=6-6x(2(13)+3x) equation:

Simplifying
4 + -9x = 6 + -6x(2(13) + 3x)

Multiply 2 * 13
4 + -9x = 6 + -6x(26 + 3x)
4 + -9x = 6 + (26 * -6x + 3x * -6x)
4 + -9x = 6 + (-156x + -18x2)

Solving
4 + -9x = 6 + -156x + -18x2

Solving for variable 'x'.

Reorder the terms:
4 + -6 + -9x + 156x + 18x2 = 6 + -156x + -18x2 + -6 + 156x + 18x2

Combine like terms: 4 + -6 = -2
-2 + -9x + 156x + 18x2 = 6 + -156x + -18x2 + -6 + 156x + 18x2

Combine like terms: -9x + 156x = 147x
-2 + 147x + 18x2 = 6 + -156x + -18x2 + -6 + 156x + 18x2

Reorder the terms:
-2 + 147x + 18x2 = 6 + -6 + -156x + 156x + -18x2 + 18x2

Combine like terms: 6 + -6 = 0
-2 + 147x + 18x2 = 0 + -156x + 156x + -18x2 + 18x2
-2 + 147x + 18x2 = -156x + 156x + -18x2 + 18x2

Combine like terms: -156x + 156x = 0
-2 + 147x + 18x2 = 0 + -18x2 + 18x2
-2 + 147x + 18x2 = -18x2 + 18x2

Combine like terms: -18x2 + 18x2 = 0
-2 + 147x + 18x2 = 0

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

Divide each side by '18'.
-0.1111111111 + 8.166666667x + x2 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + 8.166666667x + 0.1111111111 + x2 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + 8.166666667x + x2 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + 8.166666667x + x2 = 0 + 0.1111111111
8.166666667x + x2 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
8.166666667x + x2 = 0.1111111111

The x term is 8.166666667x.  Take half its coefficient (4.083333334).
Square it (16.67361112) and add it to both sides.

Add '16.67361112' to each side of the equation.
8.166666667x + 16.67361112 + x2 = 0.1111111111 + 16.67361112

Reorder the terms:
16.67361112 + 8.166666667x + x2 = 0.1111111111 + 16.67361112

Combine like terms: 0.1111111111 + 16.67361112 = 16.7847222311
16.67361112 + 8.166666667x + x2 = 16.7847222311

Factor a perfect square on the left side:
(x + 4.083333334)(x + 4.083333334) = 16.7847222311

Calculate the square root of the right side: 4.096916186

Break this problem into two subproblems by setting 
(x + 4.083333334) equal to 4.096916186 and -4.096916186.

Subproblem 1
x + 4.083333334 = 4.096916186

Simplifying
x + 4.083333334 = 4.096916186

Reorder the terms:
4.083333334 + x = 4.096916186

Solving
4.083333334 + x = 4.096916186

Solving for variable 'x'.

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

Add '-4.083333334' to each side of the equation.
4.083333334 + -4.083333334 + x = 4.096916186 + -4.083333334

Combine like terms: 4.083333334 + -4.083333334 = 0.000000000
0.000000000 + x = 4.096916186 + -4.083333334
x = 4.096916186 + -4.083333334

Combine like terms: 4.096916186 + -4.083333334 = 0.013582852
x = 0.013582852

Simplifying
x = 0.013582852

Subproblem 2
x + 4.083333334 = -4.096916186

Simplifying
x + 4.083333334 = -4.096916186

Reorder the terms:
4.083333334 + x = -4.096916186

Solving
4.083333334 + x = -4.096916186

Solving for variable 'x'.

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

Add '-4.083333334' to each side of the equation.
4.083333334 + -4.083333334 + x = -4.096916186 + -4.083333334

Combine like terms: 4.083333334 + -4.083333334 = 0.000000000
0.000000000 + x = -4.096916186 + -4.083333334
x = -4.096916186 + -4.083333334

Combine like terms: -4.096916186 + -4.083333334 = -8.18024952
x = -8.18024952

Simplifying
x = -8.18024952

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.013582852, -8.18024952}