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

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

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

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

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

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

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

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

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

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

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

Combine like terms: -1x + 6x = 5x
2 + 4x = (-3 + 5x + 2x2)

Solving
2 + 4x = -3 + 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
2 + 3 + 4x + -5x + -2x2 = -3 + 5x + 2x2 + 3 + -5x + -2x2

Combine like terms: 2 + 3 = 5
5 + 4x + -5x + -2x2 = -3 + 5x + 2x2 + 3 + -5x + -2x2

Combine like terms: 4x + -5x = -1x
5 + -1x + -2x2 = -3 + 5x + 2x2 + 3 + -5x + -2x2

Reorder the terms:
5 + -1x + -2x2 = -3 + 3 + 5x + -5x + 2x2 + -2x2

Combine like terms: -3 + 3 = 0
5 + -1x + -2x2 = 0 + 5x + -5x + 2x2 + -2x2
5 + -1x + -2x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
5 + -1x + -2x2 = 0 + 2x2 + -2x2
5 + -1x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5 + -1x + -2x2 = 0

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

Divide each side by '-2'.
-2.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 0.5x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 0.5x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 0.5x + x2 = 0 + 2.5
0.5x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
0.5x + x2 = 2.5

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 2.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 2.5 + 0.0625

Combine like terms: 2.5 + 0.0625 = 2.5625
0.0625 + 0.5x + x2 = 2.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.600781059 and -1.600781059.

Subproblem 1
x + 0.25 = 1.600781059

Simplifying
x + 0.25 = 1.600781059

Reorder the terms:
0.25 + x = 1.600781059

Solving
0.25 + x = 1.600781059

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 1.600781059 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 1.600781059 + -0.25
x = 1.600781059 + -0.25

Combine like terms: 1.600781059 + -0.25 = 1.350781059
x = 1.350781059

Simplifying
x = 1.350781059

Subproblem 2
x + 0.25 = -1.600781059

Simplifying
x + 0.25 = -1.600781059

Reorder the terms:
0.25 + x = -1.600781059

Solving
0.25 + x = -1.600781059

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -1.600781059 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -1.600781059 + -0.25
x = -1.600781059 + -0.25

Combine like terms: -1.600781059 + -0.25 = -1.850781059
x = -1.850781059

Simplifying
x = -1.850781059

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.350781059, -1.850781059}