2(x+1)-3(x-1)=(x+1)2-x(x+2)+6

Solution for 2(x+1)-3(x-1)=(x+1)2-x(x+2)+6 equation:

Simplifying
2(x + 1) + -3(x + -1) = (x + 1) * 2 + -1x(x + 2) + 6

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

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

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

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

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

Reorder the terms:
5 + -1x = (1 + x) * 2 + -1x(x + 2) + 6

Reorder the terms for easier multiplication:
5 + -1x = 2(1 + x) + -1x(x + 2) + 6
5 + -1x = (1 * 2 + x * 2) + -1x(x + 2) + 6
5 + -1x = (2 + 2x) + -1x(x + 2) + 6

Reorder the terms:
5 + -1x = 2 + 2x + -1x(2 + x) + 6
5 + -1x = 2 + 2x + (2 * -1x + x * -1x) + 6
5 + -1x = 2 + 2x + (-2x + -1x2) + 6

Reorder the terms:
5 + -1x = 2 + 6 + 2x + -2x + -1x2

Combine like terms: 2 + 6 = 8
5 + -1x = 8 + 2x + -2x + -1x2

Combine like terms: 2x + -2x = 0
5 + -1x = 8 + 0 + -1x2
5 + -1x = 8 + -1x2

Solving
5 + -1x = 8 + -1x2

Solving for variable 'x'.

Reorder the terms:
5 + -8 + -1x + x2 = 8 + -1x2 + -8 + x2

Combine like terms: 5 + -8 = -3
-3 + -1x + x2 = 8 + -1x2 + -8 + x2

Reorder the terms:
-3 + -1x + x2 = 8 + -8 + -1x2 + x2

Combine like terms: 8 + -8 = 0
-3 + -1x + x2 = 0 + -1x2 + x2
-3 + -1x + x2 = -1x2 + x2

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

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -1x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -1x + x2 = 0 + 3

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

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

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.
-1x + 0.25 + x2 = 3 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 3 + 0.25

Combine like terms: 3 + 0.25 = 3.25
0.25 + -1x + x2 = 3.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
x + -0.5 = 1.802775638

Simplifying
x + -0.5 = 1.802775638

Reorder the terms:
-0.5 + x = 1.802775638

Solving
-0.5 + x = 1.802775638

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 = 1.802775638 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.802775638 + 0.5
x = 1.802775638 + 0.5

Combine like terms: 1.802775638 + 0.5 = 2.302775638
x = 2.302775638

Simplifying
x = 2.302775638

Subproblem 2
x + -0.5 = -1.802775638

Simplifying
x + -0.5 = -1.802775638

Reorder the terms:
-0.5 + x = -1.802775638

Solving
-0.5 + x = -1.802775638

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 = -1.802775638 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.802775638 + 0.5
x = -1.802775638 + 0.5

Combine like terms: -1.802775638 + 0.5 = -1.302775638
x = -1.302775638

Simplifying
x = -1.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.302775638, -1.302775638}