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

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

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

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

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

Multiply (2 + x) * (2 + 2x)
(2(2 + 2x) + x(2 + 2x)) = (3x + 1)(2x + -1)
((2 * 2 + 2x * 2) + x(2 + 2x)) = (3x + 1)(2x + -1)
((4 + 4x) + x(2 + 2x)) = (3x + 1)(2x + -1)
(4 + 4x + (2 * x + 2x * x)) = (3x + 1)(2x + -1)
(4 + 4x + (2x + 2x2)) = (3x + 1)(2x + -1)

Combine like terms: 4x + 2x = 6x
(4 + 6x + 2x2) = (3x + 1)(2x + -1)

Reorder the terms:
4 + 6x + 2x2 = (1 + 3x)(2x + -1)

Reorder the terms:
4 + 6x + 2x2 = (1 + 3x)(-1 + 2x)

Multiply (1 + 3x) * (-1 + 2x)
4 + 6x + 2x2 = (1(-1 + 2x) + 3x * (-1 + 2x))
4 + 6x + 2x2 = ((-1 * 1 + 2x * 1) + 3x * (-1 + 2x))
4 + 6x + 2x2 = ((-1 + 2x) + 3x * (-1 + 2x))
4 + 6x + 2x2 = (-1 + 2x + (-1 * 3x + 2x * 3x))
4 + 6x + 2x2 = (-1 + 2x + (-3x + 6x2))

Combine like terms: 2x + -3x = -1x
4 + 6x + 2x2 = (-1 + -1x + 6x2)

Solving
4 + 6x + 2x2 = -1 + -1x + 6x2

Solving for variable 'x'.

Reorder the terms:
4 + 1 + 6x + x + 2x2 + -6x2 = -1 + -1x + 6x2 + 1 + x + -6x2

Combine like terms: 4 + 1 = 5
5 + 6x + x + 2x2 + -6x2 = -1 + -1x + 6x2 + 1 + x + -6x2

Combine like terms: 6x + x = 7x
5 + 7x + 2x2 + -6x2 = -1 + -1x + 6x2 + 1 + x + -6x2

Combine like terms: 2x2 + -6x2 = -4x2
5 + 7x + -4x2 = -1 + -1x + 6x2 + 1 + x + -6x2

Reorder the terms:
5 + 7x + -4x2 = -1 + 1 + -1x + x + 6x2 + -6x2

Combine like terms: -1 + 1 = 0
5 + 7x + -4x2 = 0 + -1x + x + 6x2 + -6x2
5 + 7x + -4x2 = -1x + x + 6x2 + -6x2

Combine like terms: -1x + x = 0
5 + 7x + -4x2 = 0 + 6x2 + -6x2
5 + 7x + -4x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
5 + 7x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-1.25 + -1.75x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -1.75x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -1.75x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -1.75x + x2 = 0 + 1.25
-1.75x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-1.75x + x2 = 1.25

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 1.25 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 1.25 + 0.765625

Combine like terms: 1.25 + 0.765625 = 2.015625
0.765625 + -1.75x + x2 = 2.015625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 2.015625

Calculate the square root of the right side: 1.419727086

Break this problem into two subproblems by setting 
(x + -0.875) equal to 1.419727086 and -1.419727086.

Subproblem 1
x + -0.875 = 1.419727086

Simplifying
x + -0.875 = 1.419727086

Reorder the terms:
-0.875 + x = 1.419727086

Solving
-0.875 + x = 1.419727086

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = 1.419727086 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = 1.419727086 + 0.875
x = 1.419727086 + 0.875

Combine like terms: 1.419727086 + 0.875 = 2.294727086
x = 2.294727086

Simplifying
x = 2.294727086

Subproblem 2
x + -0.875 = -1.419727086

Simplifying
x + -0.875 = -1.419727086

Reorder the terms:
-0.875 + x = -1.419727086

Solving
-0.875 + x = -1.419727086

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = -1.419727086 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = -1.419727086 + 0.875
x = -1.419727086 + 0.875

Combine like terms: -1.419727086 + 0.875 = -0.544727086
x = -0.544727086

Simplifying
x = -0.544727086

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.294727086, -0.544727086}