(x+7)(x-1)=(x+1)

Solution for (x+7)(x-1)=(x+1) equation:

Simplifying
(x + 7)(x + -1) = (x + 1)

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

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

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

Combine like terms: 7x + -1x = 6x
(-7 + 6x + x2) = (x + 1)

Reorder the terms:
-7 + 6x + x2 = (1 + x)

Remove parenthesis around (1 + x)
-7 + 6x + x2 = 1 + x

Solving
-7 + 6x + x2 = 1 + x

Solving for variable 'x'.

Reorder the terms:
-7 + -1 + 6x + -1x + x2 = 1 + x + -1 + -1x

Combine like terms: -7 + -1 = -8
-8 + 6x + -1x + x2 = 1 + x + -1 + -1x

Combine like terms: 6x + -1x = 5x
-8 + 5x + x2 = 1 + x + -1 + -1x

Reorder the terms:
-8 + 5x + x2 = 1 + -1 + x + -1x

Combine like terms: 1 + -1 = 0
-8 + 5x + x2 = 0 + x + -1x
-8 + 5x + x2 = x + -1x

Combine like terms: x + -1x = 0
-8 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 5x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 5x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 5x + x2 = 0 + 8
5x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
5x + x2 = 8

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 = 8 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 8 + 6.25

Combine like terms: 8 + 6.25 = 14.25
6.25 + 5x + x2 = 14.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
x + 2.5 = 3.774917218

Simplifying
x + 2.5 = 3.774917218

Reorder the terms:
2.5 + x = 3.774917218

Solving
2.5 + x = 3.774917218

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 = 3.774917218 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.774917218 + -2.5
x = 3.774917218 + -2.5

Combine like terms: 3.774917218 + -2.5 = 1.274917218
x = 1.274917218

Simplifying
x = 1.274917218

Subproblem 2
x + 2.5 = -3.774917218

Simplifying
x + 2.5 = -3.774917218

Reorder the terms:
2.5 + x = -3.774917218

Solving
2.5 + x = -3.774917218

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 = -3.774917218 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.774917218 + -2.5
x = -3.774917218 + -2.5

Combine like terms: -3.774917218 + -2.5 = -6.274917218
x = -6.274917218

Simplifying
x = -6.274917218

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.274917218, -6.274917218}