x+x+(x+1)(x+1)=(2x-1)(x+4)

Solution for x+x+(x+1)(x+1)=(2x-1)(x+4) equation:

Simplifying
x + x + (x + 1)(x + 1) = (2x + -1)(x + 4)

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

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

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

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

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

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

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

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

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

Multiply (-1 + 2x) * (4 + x)
1 + 4x + x2 = (-1(4 + x) + 2x * (4 + x))
1 + 4x + x2 = ((4 * -1 + x * -1) + 2x * (4 + x))
1 + 4x + x2 = ((-4 + -1x) + 2x * (4 + x))
1 + 4x + x2 = (-4 + -1x + (4 * 2x + x * 2x))
1 + 4x + x2 = (-4 + -1x + (8x + 2x2))

Combine like terms: -1x + 8x = 7x
1 + 4x + x2 = (-4 + 7x + 2x2)

Solving
1 + 4x + x2 = -4 + 7x + 2x2

Solving for variable 'x'.

Reorder the terms:
1 + 4 + 4x + -7x + x2 + -2x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2

Combine like terms: 1 + 4 = 5
5 + 4x + -7x + x2 + -2x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2

Combine like terms: 4x + -7x = -3x
5 + -3x + x2 + -2x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2

Combine like terms: x2 + -2x2 = -1x2
5 + -3x + -1x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2

Reorder the terms:
5 + -3x + -1x2 = -4 + 4 + 7x + -7x + 2x2 + -2x2

Combine like terms: -4 + 4 = 0
5 + -3x + -1x2 = 0 + 7x + -7x + 2x2 + -2x2
5 + -3x + -1x2 = 7x + -7x + 2x2 + -2x2

Combine like terms: 7x + -7x = 0
5 + -3x + -1x2 = 0 + 2x2 + -2x2
5 + -3x + -1x2 = 2x2 + -2x2

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

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-5 + 3x + x2 = 0

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 = 1.192582404
x = 1.192582404

Simplifying
x = 1.192582404

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 = -4.192582404
x = -4.192582404

Simplifying
x = -4.192582404

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