(2x+2)(x+1)=1

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

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

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

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

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

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

Solving
2 + 4x + 2x2 = 1

Solving for variable 'x'.

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

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

Combine like terms: 1 + -1 = 0
1 + 4x + 2x2 = 0

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

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

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 2x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 2x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 2x + x2 = 0 + -0.5
2x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
2x + x2 = -0.5

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -0.5 + 1

Reorder the terms:
1 + 2x + x2 = -0.5 + 1

Combine like terms: -0.5 + 1 = 0.5
1 + 2x + x2 = 0.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(x + 1) equal to 0.707106781 and -0.707106781.

Subproblem 1
x + 1 = 0.707106781

Simplifying
x + 1 = 0.707106781

Reorder the terms:
1 + x = 0.707106781

Solving
1 + x = 0.707106781

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 0.707106781 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0.707106781 + -1
x = 0.707106781 + -1

Combine like terms: 0.707106781 + -1 = -0.292893219
x = -0.292893219

Simplifying
x = -0.292893219

Subproblem 2
x + 1 = -0.707106781

Simplifying
x + 1 = -0.707106781

Reorder the terms:
1 + x = -0.707106781

Solving
1 + x = -0.707106781

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -0.707106781 + -1

Combine like terms: 1 + -1 = 0
0 + x = -0.707106781 + -1
x = -0.707106781 + -1

Combine like terms: -0.707106781 + -1 = -1.707106781
x = -1.707106781

Simplifying
x = -1.707106781

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.292893219, -1.707106781}