3(x-38)(4+(3x-5))=56

Solution for 3(x-38)(4+(3x-5))=56 equation:

Simplifying
3(x + -38)(4 + (3x + -5)) = 56

Reorder the terms:
3(-38 + x)(4 + (3x + -5)) = 56

Reorder the terms:
3(-38 + x)(4 + (-5 + 3x)) = 56

Remove parenthesis around (-5 + 3x)
3(-38 + x)(4 + -5 + 3x) = 56

Combine like terms: 4 + -5 = -1
3(-38 + x)(-1 + 3x) = 56

Multiply (-38 + x) * (-1 + 3x)
3(-38(-1 + 3x) + x(-1 + 3x)) = 56
3((-1 * -38 + 3x * -38) + x(-1 + 3x)) = 56
3((38 + -114x) + x(-1 + 3x)) = 56
3(38 + -114x + (-1 * x + 3x * x)) = 56
3(38 + -114x + (-1x + 3x2)) = 56

Combine like terms: -114x + -1x = -115x
3(38 + -115x + 3x2) = 56
(38 * 3 + -115x * 3 + 3x2 * 3) = 56
(114 + -345x + 9x2) = 56

Solving
114 + -345x + 9x2 = 56

Solving for variable 'x'.

Reorder the terms:
114 + -56 + -345x + 9x2 = 56 + -56

Combine like terms: 114 + -56 = 58
58 + -345x + 9x2 = 56 + -56

Combine like terms: 56 + -56 = 0
58 + -345x + 9x2 = 0

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

Divide each side by '9'.
6.444444444 + -38.33333333x + x2 = 0

Move the constant term to the right:

Add '-6.444444444' to each side of the equation.
6.444444444 + -38.33333333x + -6.444444444 + x2 = 0 + -6.444444444

Reorder the terms:
6.444444444 + -6.444444444 + -38.33333333x + x2 = 0 + -6.444444444

Combine like terms: 6.444444444 + -6.444444444 = 0.000000000
0.000000000 + -38.33333333x + x2 = 0 + -6.444444444
-38.33333333x + x2 = 0 + -6.444444444

Combine like terms: 0 + -6.444444444 = -6.444444444
-38.33333333x + x2 = -6.444444444

The x term is -38.33333333x.  Take half its coefficient (-19.16666667).
Square it (367.3611112) and add it to both sides.

Add '367.3611112' to each side of the equation.
-38.33333333x + 367.3611112 + x2 = -6.444444444 + 367.3611112

Reorder the terms:
367.3611112 + -38.33333333x + x2 = -6.444444444 + 367.3611112

Combine like terms: -6.444444444 + 367.3611112 = 360.916666756
367.3611112 + -38.33333333x + x2 = 360.916666756

Factor a perfect square on the left side:
(x + -19.16666667)(x + -19.16666667) = 360.916666756

Calculate the square root of the right side: 18.997806893

Break this problem into two subproblems by setting 
(x + -19.16666667) equal to 18.997806893 and -18.997806893.

Subproblem 1
x + -19.16666667 = 18.997806893

Simplifying
x + -19.16666667 = 18.997806893

Reorder the terms:
-19.16666667 + x = 18.997806893

Solving
-19.16666667 + x = 18.997806893

Solving for variable 'x'.

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

Add '19.16666667' to each side of the equation.
-19.16666667 + 19.16666667 + x = 18.997806893 + 19.16666667

Combine like terms: -19.16666667 + 19.16666667 = 0.00000000
0.00000000 + x = 18.997806893 + 19.16666667
x = 18.997806893 + 19.16666667

Combine like terms: 18.997806893 + 19.16666667 = 38.164473563
x = 38.164473563

Simplifying
x = 38.164473563

Subproblem 2
x + -19.16666667 = -18.997806893

Simplifying
x + -19.16666667 = -18.997806893

Reorder the terms:
-19.16666667 + x = -18.997806893

Solving
-19.16666667 + x = -18.997806893

Solving for variable 'x'.

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

Add '19.16666667' to each side of the equation.
-19.16666667 + 19.16666667 + x = -18.997806893 + 19.16666667

Combine like terms: -19.16666667 + 19.16666667 = 0.00000000
0.00000000 + x = -18.997806893 + 19.16666667
x = -18.997806893 + 19.16666667

Combine like terms: -18.997806893 + 19.16666667 = 0.168859777
x = 0.168859777

Simplifying
x = 0.168859777

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {38.164473563, 0.168859777}