3(x+1-2)x-1=(x+5)

Solution for 3(x+1-2)x-1=(x+5) equation:

Simplifying
3(x + 1 + -2) * x + -1 = (x + 5)

Reorder the terms:
3(1 + -2 + x) * x + -1 = (x + 5)

Combine like terms: 1 + -2 = -1
3(-1 + x) * x + -1 = (x + 5)

Reorder the terms for easier multiplication:
3x(-1 + x) + -1 = (x + 5)
(-1 * 3x + x * 3x) + -1 = (x + 5)
(-3x + 3x2) + -1 = (x + 5)

Reorder the terms:
-1 + -3x + 3x2 = (x + 5)

Reorder the terms:
-1 + -3x + 3x2 = (5 + x)

Remove parenthesis around (5 + x)
-1 + -3x + 3x2 = 5 + x

Solving
-1 + -3x + 3x2 = 5 + x

Solving for variable 'x'.

Reorder the terms:
-1 + -5 + -3x + -1x + 3x2 = 5 + x + -5 + -1x

Combine like terms: -1 + -5 = -6
-6 + -3x + -1x + 3x2 = 5 + x + -5 + -1x

Combine like terms: -3x + -1x = -4x
-6 + -4x + 3x2 = 5 + x + -5 + -1x

Reorder the terms:
-6 + -4x + 3x2 = 5 + -5 + x + -1x

Combine like terms: 5 + -5 = 0
-6 + -4x + 3x2 = 0 + x + -1x
-6 + -4x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
-6 + -4x + 3x2 = 0

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

Divide each side by '3'.
-2 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -1.333333333x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -1.333333333x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1.333333333x + x2 = 0 + 2
-1.333333333x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-1.333333333x + x2 = 2

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 2 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 2 + 0.4444444442

Combine like terms: 2 + 0.4444444442 = 2.4444444442
0.4444444442 + -1.333333333x + x2 = 2.4444444442

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 2.4444444442

Calculate the square root of the right side: 1.56347192

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 1.56347192 and -1.56347192.

Subproblem 1
x + -0.6666666665 = 1.56347192

Simplifying
x + -0.6666666665 = 1.56347192

Reorder the terms:
-0.6666666665 + x = 1.56347192

Solving
-0.6666666665 + x = 1.56347192

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 1.56347192 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 1.56347192 + 0.6666666665
x = 1.56347192 + 0.6666666665

Combine like terms: 1.56347192 + 0.6666666665 = 2.2301385865
x = 2.2301385865

Simplifying
x = 2.2301385865

Subproblem 2
x + -0.6666666665 = -1.56347192

Simplifying
x + -0.6666666665 = -1.56347192

Reorder the terms:
-0.6666666665 + x = -1.56347192

Solving
-0.6666666665 + x = -1.56347192

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -1.56347192 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -1.56347192 + 0.6666666665
x = -1.56347192 + 0.6666666665

Combine like terms: -1.56347192 + 0.6666666665 = -0.8968052535
x = -0.8968052535

Simplifying
x = -0.8968052535

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.2301385865, -0.8968052535}