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

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

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

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

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

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

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

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

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

Multiply (1 + x) * (1 + x)
-4 + 7x + 2x2 = (1(1 + x) + x(1 + x))
-4 + 7x + 2x2 = ((1 * 1 + x * 1) + x(1 + x))
-4 + 7x + 2x2 = ((1 + 1x) + x(1 + x))
-4 + 7x + 2x2 = (1 + 1x + (1 * x + x * x))
-4 + 7x + 2x2 = (1 + 1x + (1x + x2))

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

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

Solving for variable 'x'.

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

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

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

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

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

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

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 5 + 6.25

Combine like terms: 5 + 6.25 = 11.25
6.25 + 5x + x2 = 11.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.354101966 and -3.354101966.

Subproblem 1
x + 2.5 = 3.354101966

Simplifying
x + 2.5 = 3.354101966

Reorder the terms:
2.5 + x = 3.354101966

Solving
2.5 + x = 3.354101966

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 3.354101966 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.354101966 + -2.5
x = 3.354101966 + -2.5

Combine like terms: 3.354101966 + -2.5 = 0.854101966
x = 0.854101966

Simplifying
x = 0.854101966

Subproblem 2
x + 2.5 = -3.354101966

Simplifying
x + 2.5 = -3.354101966

Reorder the terms:
2.5 + x = -3.354101966

Solving
2.5 + x = -3.354101966

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -3.354101966 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.354101966 + -2.5
x = -3.354101966 + -2.5

Combine like terms: -3.354101966 + -2.5 = -5.854101966
x = -5.854101966

Simplifying
x = -5.854101966

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.854101966, -5.854101966}