x+(x+1)+(x+2)+(x+4)=x(x+2)-36

Solution for x+(x+1)+(x+2)+(x+4)=x(x+2)-36 equation:

Simplifying
x + (x + 1) + (x + 2) + (x + 4) = x(x + 2) + -36

Reorder the terms:
x + (1 + x) + (x + 2) + (x + 4) = x(x + 2) + -36

Remove parenthesis around (1 + x)
x + 1 + x + (x + 2) + (x + 4) = x(x + 2) + -36

Reorder the terms:
x + 1 + x + (2 + x) + (x + 4) = x(x + 2) + -36

Remove parenthesis around (2 + x)
x + 1 + x + 2 + x + (x + 4) = x(x + 2) + -36

Reorder the terms:
x + 1 + x + 2 + x + (4 + x) = x(x + 2) + -36

Remove parenthesis around (4 + x)
x + 1 + x + 2 + x + 4 + x = x(x + 2) + -36

Reorder the terms:
1 + 2 + 4 + x + x + x + x = x(x + 2) + -36

Combine like terms: 1 + 2 = 3
3 + 4 + x + x + x + x = x(x + 2) + -36

Combine like terms: 3 + 4 = 7
7 + x + x + x + x = x(x + 2) + -36

Combine like terms: x + x = 2x
7 + 2x + x + x = x(x + 2) + -36

Combine like terms: 2x + x = 3x
7 + 3x + x = x(x + 2) + -36

Combine like terms: 3x + x = 4x
7 + 4x = x(x + 2) + -36

Reorder the terms:
7 + 4x = x(2 + x) + -36
7 + 4x = (2 * x + x * x) + -36
7 + 4x = (2x + x2) + -36

Reorder the terms:
7 + 4x = -36 + 2x + x2

Solving
7 + 4x = -36 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
7 + 36 + 4x + -2x + -1x2 = -36 + 2x + x2 + 36 + -2x + -1x2

Combine like terms: 7 + 36 = 43
43 + 4x + -2x + -1x2 = -36 + 2x + x2 + 36 + -2x + -1x2

Combine like terms: 4x + -2x = 2x
43 + 2x + -1x2 = -36 + 2x + x2 + 36 + -2x + -1x2

Reorder the terms:
43 + 2x + -1x2 = -36 + 36 + 2x + -2x + x2 + -1x2

Combine like terms: -36 + 36 = 0
43 + 2x + -1x2 = 0 + 2x + -2x + x2 + -1x2
43 + 2x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
43 + 2x + -1x2 = 0 + x2 + -1x2
43 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
43 + 2x + -1x2 = 0

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

Divide each side by '-1'.
-43 + -2x + x2 = 0

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + -2x + 43 + x2 = 0 + 43

Reorder the terms:
-43 + 43 + -2x + x2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -2x + x2 = 0 + 43
-2x + x2 = 0 + 43

Combine like terms: 0 + 43 = 43
-2x + x2 = 43

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 43 + 1

Reorder the terms:
1 + -2x + x2 = 43 + 1

Combine like terms: 43 + 1 = 44
1 + -2x + x2 = 44

Factor a perfect square on the left side:
(x + -1)(x + -1) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(x + -1) equal to 6.633249581 and -6.633249581.

Subproblem 1
x + -1 = 6.633249581

Simplifying
x + -1 = 6.633249581

Reorder the terms:
-1 + x = 6.633249581

Solving
-1 + x = 6.633249581

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 6.633249581 + 1

Combine like terms: -1 + 1 = 0
0 + x = 6.633249581 + 1
x = 6.633249581 + 1

Combine like terms: 6.633249581 + 1 = 7.633249581
x = 7.633249581

Simplifying
x = 7.633249581

Subproblem 2
x + -1 = -6.633249581

Simplifying
x + -1 = -6.633249581

Reorder the terms:
-1 + x = -6.633249581

Solving
-1 + x = -6.633249581

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -6.633249581 + 1

Combine like terms: -1 + 1 = 0
0 + x = -6.633249581 + 1
x = -6.633249581 + 1

Combine like terms: -6.633249581 + 1 = -5.633249581
x = -5.633249581

Simplifying
x = -5.633249581

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.633249581, -5.633249581}