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

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

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

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

Reorder the terms for easier multiplication:
2 * 3x(2 + x) = 2(x + 1) + 1

Multiply 2 * 3
6x(2 + x) = 2(x + 1) + 1
(2 * 6x + x * 6x) = 2(x + 1) + 1
(12x + 6x2) = 2(x + 1) + 1

Reorder the terms:
12x + 6x2 = 2(1 + x) + 1
12x + 6x2 = (1 * 2 + x * 2) + 1
12x + 6x2 = (2 + 2x) + 1

Reorder the terms:
12x + 6x2 = 2 + 1 + 2x

Combine like terms: 2 + 1 = 3
12x + 6x2 = 3 + 2x

Solving
12x + 6x2 = 3 + 2x

Solving for variable 'x'.

Reorder the terms:
-3 + 12x + -2x + 6x2 = 3 + 2x + -3 + -2x

Combine like terms: 12x + -2x = 10x
-3 + 10x + 6x2 = 3 + 2x + -3 + -2x

Reorder the terms:
-3 + 10x + 6x2 = 3 + -3 + 2x + -2x

Combine like terms: 3 + -3 = 0
-3 + 10x + 6x2 = 0 + 2x + -2x
-3 + 10x + 6x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-3 + 10x + 6x2 = 0

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

Divide each side by '6'.
-0.5 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 1.666666667x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 1.666666667x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 1.666666667x + x2 = 0 + 0.5
1.666666667x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
1.666666667x + x2 = 0.5

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 0.5 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 0.5 + 0.6944444447

Combine like terms: 0.5 + 0.6944444447 = 1.1944444447
0.6944444447 + 1.666666667x + x2 = 1.1944444447

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 1.1944444447

Calculate the square root of the right side: 1.092906421

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 1.092906421 and -1.092906421.

Subproblem 1
x + 0.8333333335 = 1.092906421

Simplifying
x + 0.8333333335 = 1.092906421

Reorder the terms:
0.8333333335 + x = 1.092906421

Solving
0.8333333335 + x = 1.092906421

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 1.092906421 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 1.092906421 + -0.8333333335
x = 1.092906421 + -0.8333333335

Combine like terms: 1.092906421 + -0.8333333335 = 0.2595730875
x = 0.2595730875

Simplifying
x = 0.2595730875

Subproblem 2
x + 0.8333333335 = -1.092906421

Simplifying
x + 0.8333333335 = -1.092906421

Reorder the terms:
0.8333333335 + x = -1.092906421

Solving
0.8333333335 + x = -1.092906421

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -1.092906421 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -1.092906421 + -0.8333333335
x = -1.092906421 + -0.8333333335

Combine like terms: -1.092906421 + -0.8333333335 = -1.9262397545
x = -1.9262397545

Simplifying
x = -1.9262397545

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2595730875, -1.9262397545}