(x+6)(3x-8)+3x-1=20

Solution for (x+6)(3x-8)+3x-1=20 equation:

Simplifying
(x + 6)(3x + -8) + 3x + -1 = 20

Reorder the terms:
(6 + x)(3x + -8) + 3x + -1 = 20

Reorder the terms:
(6 + x)(-8 + 3x) + 3x + -1 = 20

Multiply (6 + x) * (-8 + 3x)
(6(-8 + 3x) + x(-8 + 3x)) + 3x + -1 = 20
((-8 * 6 + 3x * 6) + x(-8 + 3x)) + 3x + -1 = 20
((-48 + 18x) + x(-8 + 3x)) + 3x + -1 = 20
(-48 + 18x + (-8 * x + 3x * x)) + 3x + -1 = 20
(-48 + 18x + (-8x + 3x2)) + 3x + -1 = 20

Combine like terms: 18x + -8x = 10x
(-48 + 10x + 3x2) + 3x + -1 = 20

Reorder the terms:
-48 + -1 + 10x + 3x + 3x2 = 20

Combine like terms: -48 + -1 = -49
-49 + 10x + 3x + 3x2 = 20

Combine like terms: 10x + 3x = 13x
-49 + 13x + 3x2 = 20

Solving
-49 + 13x + 3x2 = 20

Solving for variable 'x'.

Reorder the terms:
-49 + -20 + 13x + 3x2 = 20 + -20

Combine like terms: -49 + -20 = -69
-69 + 13x + 3x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-69 + 13x + 3x2 = 0

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

Divide each side by '3'.
-23 + 4.333333333x + x2 = 0

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + 4.333333333x + 23 + x2 = 0 + 23

Reorder the terms:
-23 + 23 + 4.333333333x + x2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 4.333333333x + x2 = 0 + 23
4.333333333x + x2 = 0 + 23

Combine like terms: 0 + 23 = 23
4.333333333x + x2 = 23

The x term is 4.333333333x.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333x + 4.694444446 + x2 = 23 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333x + x2 = 23 + 4.694444446

Combine like terms: 23 + 4.694444446 = 27.694444446
4.694444446 + 4.333333333x + x2 = 27.694444446

Factor a perfect square on the left side:
(x + 2.166666667)(x + 2.166666667) = 27.694444446

Calculate the square root of the right side: 5.262551135

Break this problem into two subproblems by setting 
(x + 2.166666667) equal to 5.262551135 and -5.262551135.

Subproblem 1
x + 2.166666667 = 5.262551135

Simplifying
x + 2.166666667 = 5.262551135

Reorder the terms:
2.166666667 + x = 5.262551135

Solving
2.166666667 + x = 5.262551135

Solving for variable 'x'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x = 5.262551135 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x = 5.262551135 + -2.166666667
x = 5.262551135 + -2.166666667

Combine like terms: 5.262551135 + -2.166666667 = 3.095884468
x = 3.095884468

Simplifying
x = 3.095884468

Subproblem 2
x + 2.166666667 = -5.262551135

Simplifying
x + 2.166666667 = -5.262551135

Reorder the terms:
2.166666667 + x = -5.262551135

Solving
2.166666667 + x = -5.262551135

Solving for variable 'x'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x = -5.262551135 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x = -5.262551135 + -2.166666667
x = -5.262551135 + -2.166666667

Combine like terms: -5.262551135 + -2.166666667 = -7.429217802
x = -7.429217802

Simplifying
x = -7.429217802

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.095884468, -7.429217802}