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

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

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

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

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

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

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

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

Reorder the terms for easier multiplication:
-6 + -4x + 2x2 + -1 * 2(1 + x) = 2

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

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

Combine like terms: -6 + -2 = -8
-8 + -4x + -2x + 2x2 = 2

Combine like terms: -4x + -2x = -6x
-8 + -6x + 2x2 = 2

Solving
-8 + -6x + 2x2 = 2

Solving for variable 'x'.

Reorder the terms:
-8 + -2 + -6x + 2x2 = 2 + -2

Combine like terms: -8 + -2 = -10
-10 + -6x + 2x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-10 + -6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -3x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
-5 + -3x + x2 = 0

Solving
-5 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -3x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -3x + x2 = 0 + 5

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

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

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 = 5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 5 + 2.25

Combine like terms: 5 + 2.25 = 7.25
2.25 + -3x + x2 = 7.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.692582404 and -2.692582404.

Subproblem 1
x + -1.5 = 2.692582404

Simplifying
x + -1.5 = 2.692582404

Reorder the terms:
-1.5 + x = 2.692582404

Solving
-1.5 + x = 2.692582404

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 = 2.692582404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.692582404 + 1.5
x = 2.692582404 + 1.5

Combine like terms: 2.692582404 + 1.5 = 4.192582404
x = 4.192582404

Simplifying
x = 4.192582404

Subproblem 2
x + -1.5 = -2.692582404

Simplifying
x + -1.5 = -2.692582404

Reorder the terms:
-1.5 + x = -2.692582404

Solving
-1.5 + x = -2.692582404

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 = -2.692582404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.692582404 + 1.5
x = -2.692582404 + 1.5

Combine like terms: -2.692582404 + 1.5 = -1.192582404
x = -1.192582404

Simplifying
x = -1.192582404

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.192582404, -1.192582404}
Solution
x = {4.192582404, -1.192582404}