(x+3)2+5=(x+5)(x-5)+(x-4)

Solution for (x+3)2+5=(x+5)(x-5)+(x-4) equation:

Simplifying
(x + 3) * 2 + 5 = (x + 5)(x + -5) + (x + -4)

Reorder the terms:
(3 + x) * 2 + 5 = (x + 5)(x + -5) + (x + -4)

Reorder the terms for easier multiplication:
2(3 + x) + 5 = (x + 5)(x + -5) + (x + -4)
(3 * 2 + x * 2) + 5 = (x + 5)(x + -5) + (x + -4)
(6 + 2x) + 5 = (x + 5)(x + -5) + (x + -4)

Reorder the terms:
6 + 5 + 2x = (x + 5)(x + -5) + (x + -4)

Combine like terms: 6 + 5 = 11
11 + 2x = (x + 5)(x + -5) + (x + -4)

Reorder the terms:
11 + 2x = (5 + x)(x + -5) + (x + -4)

Reorder the terms:
11 + 2x = (5 + x)(-5 + x) + (x + -4)

Multiply (5 + x) * (-5 + x)
11 + 2x = (5(-5 + x) + x(-5 + x)) + (x + -4)
11 + 2x = ((-5 * 5 + x * 5) + x(-5 + x)) + (x + -4)
11 + 2x = ((-25 + 5x) + x(-5 + x)) + (x + -4)
11 + 2x = (-25 + 5x + (-5 * x + x * x)) + (x + -4)
11 + 2x = (-25 + 5x + (-5x + x2)) + (x + -4)

Combine like terms: 5x + -5x = 0
11 + 2x = (-25 + 0 + x2) + (x + -4)
11 + 2x = (-25 + x2) + (x + -4)

Reorder the terms:
11 + 2x = -25 + x2 + (-4 + x)

Remove parenthesis around (-4 + x)
11 + 2x = -25 + x2 + -4 + x

Reorder the terms:
11 + 2x = -25 + -4 + x + x2

Combine like terms: -25 + -4 = -29
11 + 2x = -29 + x + x2

Solving
11 + 2x = -29 + x + x2

Solving for variable 'x'.

Reorder the terms:
11 + 29 + 2x + -1x + -1x2 = -29 + x + x2 + 29 + -1x + -1x2

Combine like terms: 11 + 29 = 40
40 + 2x + -1x + -1x2 = -29 + x + x2 + 29 + -1x + -1x2

Combine like terms: 2x + -1x = 1x
40 + 1x + -1x2 = -29 + x + x2 + 29 + -1x + -1x2

Reorder the terms:
40 + 1x + -1x2 = -29 + 29 + x + -1x + x2 + -1x2

Combine like terms: -29 + 29 = 0
40 + 1x + -1x2 = 0 + x + -1x + x2 + -1x2
40 + 1x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
40 + 1x + -1x2 = 0 + x2 + -1x2
40 + 1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
40 + 1x + -1x2 = 0

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

Divide each side by '-1'.
-40 + -1x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -1x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -1x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -1x + x2 = 0 + 40
-1x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-1x + x2 = 40

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 40 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 40 + 0.25

Combine like terms: 40 + 0.25 = 40.25
0.25 + -1x + x2 = 40.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(x + -0.5) equal to 6.34428877 and -6.34428877.

Subproblem 1
x + -0.5 = 6.34428877

Simplifying
x + -0.5 = 6.34428877

Reorder the terms:
-0.5 + x = 6.34428877

Solving
-0.5 + x = 6.34428877

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 6.34428877 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 6.34428877 + 0.5
x = 6.34428877 + 0.5

Combine like terms: 6.34428877 + 0.5 = 6.84428877
x = 6.84428877

Simplifying
x = 6.84428877

Subproblem 2
x + -0.5 = -6.34428877

Simplifying
x + -0.5 = -6.34428877

Reorder the terms:
-0.5 + x = -6.34428877

Solving
-0.5 + x = -6.34428877

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -6.34428877 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -6.34428877 + 0.5
x = -6.34428877 + 0.5

Combine like terms: -6.34428877 + 0.5 = -5.84428877
x = -5.84428877

Simplifying
x = -5.84428877

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.84428877, -5.84428877}