2(x+3)2x=22

Solution for 2(x+3)2x=22 equation:

Simplifying
2(x + 3) * 2x = 22

Reorder the terms:
2(3 + x) * 2x = 22

Reorder the terms for easier multiplication:
2 * 2x(3 + x) = 22

Multiply 2 * 2
4x(3 + x) = 22
(3 * 4x + x * 4x) = 22
(12x + 4x2) = 22

Solving
12x + 4x2 = 22

Solving for variable 'x'.

Reorder the terms:
-22 + 12x + 4x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-22 + 12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + 6x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-11 + 6x + 2x2)' equal to zero and attempt to solve:

Simplifying
-11 + 6x + 2x2 = 0

Solving
-11 + 6x + 2x2 = 0

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

Divide each side by '2'.
-5.5 + 3x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + 3x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + 3x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + 3x + x2 = 0 + 5.5
3x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
3x + x2 = 5.5

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 5.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 5.5 + 2.25

Combine like terms: 5.5 + 2.25 = 7.75
2.25 + 3x + x2 = 7.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 7.75

Calculate the square root of the right side: 2.783882181

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.783882181 and -2.783882181.

Subproblem 1
x + 1.5 = 2.783882181

Simplifying
x + 1.5 = 2.783882181

Reorder the terms:
1.5 + x = 2.783882181

Solving
1.5 + x = 2.783882181

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 2.783882181 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2.783882181 + -1.5
x = 2.783882181 + -1.5

Combine like terms: 2.783882181 + -1.5 = 1.283882181
x = 1.283882181

Simplifying
x = 1.283882181

Subproblem 2
x + 1.5 = -2.783882181

Simplifying
x + 1.5 = -2.783882181

Reorder the terms:
1.5 + x = -2.783882181

Solving
1.5 + x = -2.783882181

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -2.783882181 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2.783882181 + -1.5
x = -2.783882181 + -1.5

Combine like terms: -2.783882181 + -1.5 = -4.283882181
x = -4.283882181

Simplifying
x = -4.283882181

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.283882181, -4.283882181}
Solution
x = {1.283882181, -4.283882181}