3x[4x-3(x+5)]+19=2(x-23)

Solution for 3x[4x-3(x+5)]+19=2(x-23) equation:

Simplifying
3x[4x + -3(x + 5)] + 19 = 2(x + -23)

Reorder the terms:
3x[4x + -3(5 + x)] + 19 = 2(x + -23)
3x[4x + (5 * -3 + x * -3)] + 19 = 2(x + -23)
3x[4x + (-15 + -3x)] + 19 = 2(x + -23)

Reorder the terms:
3x[-15 + 4x + -3x] + 19 = 2(x + -23)

Combine like terms: 4x + -3x = 1x
3x[-15 + 1x] + 19 = 2(x + -23)
[-15 * 3x + 1x * 3x] + 19 = 2(x + -23)
[-45x + 3x2] + 19 = 2(x + -23)

Reorder the terms:
19 + -45x + 3x2 = 2(x + -23)

Reorder the terms:
19 + -45x + 3x2 = 2(-23 + x)
19 + -45x + 3x2 = (-23 * 2 + x * 2)
19 + -45x + 3x2 = (-46 + 2x)

Solving
19 + -45x + 3x2 = -46 + 2x

Solving for variable 'x'.

Reorder the terms:
19 + 46 + -45x + -2x + 3x2 = -46 + 2x + 46 + -2x

Combine like terms: 19 + 46 = 65
65 + -45x + -2x + 3x2 = -46 + 2x + 46 + -2x

Combine like terms: -45x + -2x = -47x
65 + -47x + 3x2 = -46 + 2x + 46 + -2x

Reorder the terms:
65 + -47x + 3x2 = -46 + 46 + 2x + -2x

Combine like terms: -46 + 46 = 0
65 + -47x + 3x2 = 0 + 2x + -2x
65 + -47x + 3x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
65 + -47x + 3x2 = 0

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

Divide each side by '3'.
21.66666667 + -15.66666667x + x2 = 0

Move the constant term to the right:

Add '-21.66666667' to each side of the equation.
21.66666667 + -15.66666667x + -21.66666667 + x2 = 0 + -21.66666667

Reorder the terms:
21.66666667 + -21.66666667 + -15.66666667x + x2 = 0 + -21.66666667

Combine like terms: 21.66666667 + -21.66666667 = 0.00000000
0.00000000 + -15.66666667x + x2 = 0 + -21.66666667
-15.66666667x + x2 = 0 + -21.66666667

Combine like terms: 0 + -21.66666667 = -21.66666667
-15.66666667x + x2 = -21.66666667

The x term is -15.66666667x.  Take half its coefficient (-7.833333335).
Square it (61.36111114) and add it to both sides.

Add '61.36111114' to each side of the equation.
-15.66666667x + 61.36111114 + x2 = -21.66666667 + 61.36111114

Reorder the terms:
61.36111114 + -15.66666667x + x2 = -21.66666667 + 61.36111114

Combine like terms: -21.66666667 + 61.36111114 = 39.69444447
61.36111114 + -15.66666667x + x2 = 39.69444447

Factor a perfect square on the left side:
(x + -7.833333335)(x + -7.833333335) = 39.69444447

Calculate the square root of the right side: 6.300352726

Break this problem into two subproblems by setting 
(x + -7.833333335) equal to 6.300352726 and -6.300352726.

Subproblem 1
x + -7.833333335 = 6.300352726

Simplifying
x + -7.833333335 = 6.300352726

Reorder the terms:
-7.833333335 + x = 6.300352726

Solving
-7.833333335 + x = 6.300352726

Solving for variable 'x'.

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

Add '7.833333335' to each side of the equation.
-7.833333335 + 7.833333335 + x = 6.300352726 + 7.833333335

Combine like terms: -7.833333335 + 7.833333335 = 0.000000000
0.000000000 + x = 6.300352726 + 7.833333335
x = 6.300352726 + 7.833333335

Combine like terms: 6.300352726 + 7.833333335 = 14.133686061
x = 14.133686061

Simplifying
x = 14.133686061

Subproblem 2
x + -7.833333335 = -6.300352726

Simplifying
x + -7.833333335 = -6.300352726

Reorder the terms:
-7.833333335 + x = -6.300352726

Solving
-7.833333335 + x = -6.300352726

Solving for variable 'x'.

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

Add '7.833333335' to each side of the equation.
-7.833333335 + 7.833333335 + x = -6.300352726 + 7.833333335

Combine like terms: -7.833333335 + 7.833333335 = 0.000000000
0.000000000 + x = -6.300352726 + 7.833333335
x = -6.300352726 + 7.833333335

Combine like terms: -6.300352726 + 7.833333335 = 1.532980609
x = 1.532980609

Simplifying
x = 1.532980609

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.133686061, 1.532980609}