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

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

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

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

Reorder the terms for easier multiplication:
x(1 + x) + -2(x + 3) = (2 + x) + -3x
(1 * x + x * x) + -2(x + 3) = (2 + x) + -3x
(1x + x2) + -2(x + 3) = (2 + x) + -3x

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

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

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

Remove parenthesis around (2 + x)
-6 + -1x + x2 = 2 + x + -3x

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

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

Solving for variable 'x'.

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

Combine like terms: -6 + -2 = -8
-8 + -1x + 2x + x2 = 2 + -2x + -2 + 2x

Combine like terms: -1x + 2x = 1x
-8 + 1x + x2 = 2 + -2x + -2 + 2x

Reorder the terms:
-8 + 1x + x2 = 2 + -2 + -2x + 2x

Combine like terms: 2 + -2 = 0
-8 + 1x + x2 = 0 + -2x + 2x
-8 + 1x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-8 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 1x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 1x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 1x + x2 = 0 + 8
1x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
1x + x2 = 8

The x term is 1x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 8 + 0.25

Reorder the terms:
0.25 + x + x2 = 8 + 0.25

Combine like terms: 8 + 0.25 = 8.25
0.25 + x + x2 = 8.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.872281323 and -2.872281323.

Subproblem 1
x + 0.5 = 2.872281323

Simplifying
x + 0.5 = 2.872281323

Reorder the terms:
0.5 + x = 2.872281323

Solving
0.5 + x = 2.872281323

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 2.872281323 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.872281323 + -0.5
x = 2.872281323 + -0.5

Combine like terms: 2.872281323 + -0.5 = 2.372281323
x = 2.372281323

Simplifying
x = 2.372281323

Subproblem 2
x + 0.5 = -2.872281323

Simplifying
x + 0.5 = -2.872281323

Reorder the terms:
0.5 + x = -2.872281323

Solving
0.5 + x = -2.872281323

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -2.872281323 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.872281323 + -0.5
x = -2.872281323 + -0.5

Combine like terms: -2.872281323 + -0.5 = -3.372281323
x = -3.372281323

Simplifying
x = -3.372281323

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.372281323, -3.372281323}