3x[8-3(x-1)]=x+19

Solution for 3x[8-3(x-1)]=x+19 equation:

Simplifying
3x[8 + -3(x + -1)] = x + 19

Reorder the terms:
3x[8 + -3(-1 + x)] = x + 19
3x[8 + (-1 * -3 + x * -3)] = x + 19
3x[8 + (3 + -3x)] = x + 19

Combine like terms: 8 + 3 = 11
3x[11 + -3x] = x + 19
[11 * 3x + -3x * 3x] = x + 19
[33x + -9x2] = x + 19

Reorder the terms:
33x + -9x2 = 19 + x

Solving
33x + -9x2 = 19 + x

Solving for variable 'x'.

Reorder the terms:
-19 + 33x + -1x + -9x2 = 19 + x + -19 + -1x

Combine like terms: 33x + -1x = 32x
-19 + 32x + -9x2 = 19 + x + -19 + -1x

Reorder the terms:
-19 + 32x + -9x2 = 19 + -19 + x + -1x

Combine like terms: 19 + -19 = 0
-19 + 32x + -9x2 = 0 + x + -1x
-19 + 32x + -9x2 = x + -1x

Combine like terms: x + -1x = 0
-19 + 32x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
2.111111111 + -3.555555556x + x2 = 0

Move the constant term to the right:

Add '-2.111111111' to each side of the equation.
2.111111111 + -3.555555556x + -2.111111111 + x2 = 0 + -2.111111111

Reorder the terms:
2.111111111 + -2.111111111 + -3.555555556x + x2 = 0 + -2.111111111

Combine like terms: 2.111111111 + -2.111111111 = 0.000000000
0.000000000 + -3.555555556x + x2 = 0 + -2.111111111
-3.555555556x + x2 = 0 + -2.111111111

Combine like terms: 0 + -2.111111111 = -2.111111111
-3.555555556x + x2 = -2.111111111

The x term is -3.555555556x.  Take half its coefficient (-1.777777778).
Square it (3.160493828) and add it to both sides.

Add '3.160493828' to each side of the equation.
-3.555555556x + 3.160493828 + x2 = -2.111111111 + 3.160493828

Reorder the terms:
3.160493828 + -3.555555556x + x2 = -2.111111111 + 3.160493828

Combine like terms: -2.111111111 + 3.160493828 = 1.049382717
3.160493828 + -3.555555556x + x2 = 1.049382717

Factor a perfect square on the left side:
(x + -1.777777778)(x + -1.777777778) = 1.049382717

Calculate the square root of the right side: 1.024393829

Break this problem into two subproblems by setting 
(x + -1.777777778) equal to 1.024393829 and -1.024393829.

Subproblem 1
x + -1.777777778 = 1.024393829

Simplifying
x + -1.777777778 = 1.024393829

Reorder the terms:
-1.777777778 + x = 1.024393829

Solving
-1.777777778 + x = 1.024393829

Solving for variable 'x'.

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

Add '1.777777778' to each side of the equation.
-1.777777778 + 1.777777778 + x = 1.024393829 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + x = 1.024393829 + 1.777777778
x = 1.024393829 + 1.777777778

Combine like terms: 1.024393829 + 1.777777778 = 2.802171607
x = 2.802171607

Simplifying
x = 2.802171607

Subproblem 2
x + -1.777777778 = -1.024393829

Simplifying
x + -1.777777778 = -1.024393829

Reorder the terms:
-1.777777778 + x = -1.024393829

Solving
-1.777777778 + x = -1.024393829

Solving for variable 'x'.

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

Add '1.777777778' to each side of the equation.
-1.777777778 + 1.777777778 + x = -1.024393829 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + x = -1.024393829 + 1.777777778
x = -1.024393829 + 1.777777778

Combine like terms: -1.024393829 + 1.777777778 = 0.753383949
x = 0.753383949

Simplifying
x = 0.753383949

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.802171607, 0.753383949}