(x+5)(x-1)=(x+1)

Solution for (x+5)(x-1)=(x+1) equation:

Simplifying
(x + 5)(x + -1) = (x + 1)

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

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

Multiply (5 + x) * (-1 + x)
(5(-1 + x) + x(-1 + x)) = (x + 1)
((-1 * 5 + x * 5) + x(-1 + x)) = (x + 1)
((-5 + 5x) + x(-1 + x)) = (x + 1)
(-5 + 5x + (-1 * x + x * x)) = (x + 1)
(-5 + 5x + (-1x + x2)) = (x + 1)

Combine like terms: 5x + -1x = 4x
(-5 + 4x + x2) = (x + 1)

Reorder the terms:
-5 + 4x + x2 = (1 + x)

Remove parenthesis around (1 + x)
-5 + 4x + x2 = 1 + x

Solving
-5 + 4x + x2 = 1 + x

Solving for variable 'x'.

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

Combine like terms: -5 + -1 = -6
-6 + 4x + -1x + x2 = 1 + x + -1 + -1x

Combine like terms: 4x + -1x = 3x
-6 + 3x + x2 = 1 + x + -1 + -1x

Reorder the terms:
-6 + 3x + x2 = 1 + -1 + x + -1x

Combine like terms: 1 + -1 = 0
-6 + 3x + x2 = 0 + x + -1x
-6 + 3x + x2 = x + -1x

Combine like terms: x + -1x = 0
-6 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 3x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 3x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 3x + x2 = 0 + 6
3x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
3x + x2 = 6

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 = 6 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 6 + 2.25

Combine like terms: 6 + 2.25 = 8.25
2.25 + 3x + x2 = 8.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.872281323 and -2.872281323.

Subproblem 1
x + 1.5 = 2.872281323

Simplifying
x + 1.5 = 2.872281323

Reorder the terms:
1.5 + x = 2.872281323

Solving
1.5 + x = 2.872281323

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 = 2.872281323 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2.872281323 + -1.5
x = 2.872281323 + -1.5

Combine like terms: 2.872281323 + -1.5 = 1.372281323
x = 1.372281323

Simplifying
x = 1.372281323

Subproblem 2
x + 1.5 = -2.872281323

Simplifying
x + 1.5 = -2.872281323

Reorder the terms:
1.5 + x = -2.872281323

Solving
1.5 + x = -2.872281323

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 = -2.872281323 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2.872281323 + -1.5
x = -2.872281323 + -1.5

Combine like terms: -2.872281323 + -1.5 = -4.372281323
x = -4.372281323

Simplifying
x = -4.372281323

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.372281323, -4.372281323}