x+1(x+1+5)=x(x+8)

Solution for x+1(x+1+5)=x(x+8) equation:

Simplifying
x + 1(x + 1 + 5) = x(x + 8)

Reorder the terms:
x + 1(1 + 5 + x) = x(x + 8)

Combine like terms: 1 + 5 = 6
x + 1(6 + x) = x(x + 8)
x + (6 * 1 + x * 1) = x(x + 8)
x + (6 + 1x) = x(x + 8)

Reorder the terms:
6 + x + 1x = x(x + 8)

Combine like terms: x + 1x = 2x
6 + 2x = x(x + 8)

Reorder the terms:
6 + 2x = x(8 + x)
6 + 2x = (8 * x + x * x)
6 + 2x = (8x + x2)

Solving
6 + 2x = 8x + x2

Solving for variable 'x'.

Combine like terms: 2x + -8x = -6x
6 + -6x + -1x2 = 8x + x2 + -8x + -1x2

Reorder the terms:
6 + -6x + -1x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
6 + -6x + -1x2 = 0 + x2 + -1x2
6 + -6x + -1x2 = x2 + -1x2

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

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

Divide each side by '-1'.
-6 + 6x + x2 = 0

Move the constant term to the right:

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

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

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

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

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 6 + 9

Reorder the terms:
9 + 6x + x2 = 6 + 9

Combine like terms: 6 + 9 = 15
9 + 6x + x2 = 15

Factor a perfect square on the left side:
(x + 3)(x + 3) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + 3) equal to 3.872983346 and -3.872983346.

Subproblem 1
x + 3 = 3.872983346

Simplifying
x + 3 = 3.872983346

Reorder the terms:
3 + x = 3.872983346

Solving
3 + x = 3.872983346

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 3.872983346 + -3

Combine like terms: 3 + -3 = 0
0 + x = 3.872983346 + -3
x = 3.872983346 + -3

Combine like terms: 3.872983346 + -3 = 0.872983346
x = 0.872983346

Simplifying
x = 0.872983346

Subproblem 2
x + 3 = -3.872983346

Simplifying
x + 3 = -3.872983346

Reorder the terms:
3 + x = -3.872983346

Solving
3 + x = -3.872983346

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -3.872983346 + -3

Combine like terms: 3 + -3 = 0
0 + x = -3.872983346 + -3
x = -3.872983346 + -3

Combine like terms: -3.872983346 + -3 = -6.872983346
x = -6.872983346

Simplifying
x = -6.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.872983346, -6.872983346}