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

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

Simplifying
x + 2 + 2(x + 2) = 3x(x + -2)

Reorder the terms:
x + 2 + 2(2 + x) = 3x(x + -2)
x + 2 + (2 * 2 + x * 2) = 3x(x + -2)
x + 2 + (4 + 2x) = 3x(x + -2)

Reorder the terms:
2 + 4 + x + 2x = 3x(x + -2)

Combine like terms: 2 + 4 = 6
6 + x + 2x = 3x(x + -2)

Combine like terms: x + 2x = 3x
6 + 3x = 3x(x + -2)

Reorder the terms:
6 + 3x = 3x(-2 + x)
6 + 3x = (-2 * 3x + x * 3x)
6 + 3x = (-6x + 3x2)

Solving
6 + 3x = -6x + 3x2

Solving for variable 'x'.

Combine like terms: 3x + 6x = 9x
6 + 9x + -3x2 = -6x + 3x2 + 6x + -3x2

Reorder the terms:
6 + 9x + -3x2 = -6x + 6x + 3x2 + -3x2

Combine like terms: -6x + 6x = 0
6 + 9x + -3x2 = 0 + 3x2 + -3x2
6 + 9x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
6 + 9x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 3x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + 3x + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + 3x + -1x2 = 0

Solving
2 + 3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + -3x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -3x + x2 = 0 + 2

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

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

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 = 2 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + -3x + x2 = 4.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
x + -1.5 = 2.061552813

Simplifying
x + -1.5 = 2.061552813

Reorder the terms:
-1.5 + x = 2.061552813

Solving
-1.5 + x = 2.061552813

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 = 2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.061552813 + 1.5
x = 2.061552813 + 1.5

Combine like terms: 2.061552813 + 1.5 = 3.561552813
x = 3.561552813

Simplifying
x = 3.561552813

Subproblem 2
x + -1.5 = -2.061552813

Simplifying
x + -1.5 = -2.061552813

Reorder the terms:
-1.5 + x = -2.061552813

Solving
-1.5 + x = -2.061552813

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 = -2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.061552813 + 1.5
x = -2.061552813 + 1.5

Combine like terms: -2.061552813 + 1.5 = -0.561552813
x = -0.561552813

Simplifying
x = -0.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.561552813, -0.561552813}
Solution
x = {3.561552813, -0.561552813}