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

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

Simplifying
(x + 3) * 2 + 5 = (x + 5)(x + -5) + (4 + -1x)

Reorder the terms:
(3 + x) * 2 + 5 = (x + 5)(x + -5) + (4 + -1x)

Reorder the terms for easier multiplication:
2(3 + x) + 5 = (x + 5)(x + -5) + (4 + -1x)
(3 * 2 + x * 2) + 5 = (x + 5)(x + -5) + (4 + -1x)
(6 + 2x) + 5 = (x + 5)(x + -5) + (4 + -1x)

Reorder the terms:
6 + 5 + 2x = (x + 5)(x + -5) + (4 + -1x)

Combine like terms: 6 + 5 = 11
11 + 2x = (x + 5)(x + -5) + (4 + -1x)

Reorder the terms:
11 + 2x = (5 + x)(x + -5) + (4 + -1x)

Reorder the terms:
11 + 2x = (5 + x)(-5 + x) + (4 + -1x)

Multiply (5 + x) * (-5 + x)
11 + 2x = (5(-5 + x) + x(-5 + x)) + (4 + -1x)
11 + 2x = ((-5 * 5 + x * 5) + x(-5 + x)) + (4 + -1x)
11 + 2x = ((-25 + 5x) + x(-5 + x)) + (4 + -1x)
11 + 2x = (-25 + 5x + (-5 * x + x * x)) + (4 + -1x)
11 + 2x = (-25 + 5x + (-5x + x2)) + (4 + -1x)

Combine like terms: 5x + -5x = 0
11 + 2x = (-25 + 0 + x2) + (4 + -1x)
11 + 2x = (-25 + x2) + (4 + -1x)

Remove parenthesis around (4 + -1x)
11 + 2x = -25 + x2 + 4 + -1x

Reorder the terms:
11 + 2x = -25 + 4 + -1x + x2

Combine like terms: -25 + 4 = -21
11 + 2x = -21 + -1x + x2

Solving
11 + 2x = -21 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
11 + 21 + 2x + x + -1x2 = -21 + -1x + x2 + 21 + x + -1x2

Combine like terms: 11 + 21 = 32
32 + 2x + x + -1x2 = -21 + -1x + x2 + 21 + x + -1x2

Combine like terms: 2x + x = 3x
32 + 3x + -1x2 = -21 + -1x + x2 + 21 + x + -1x2

Reorder the terms:
32 + 3x + -1x2 = -21 + 21 + -1x + x + x2 + -1x2

Combine like terms: -21 + 21 = 0
32 + 3x + -1x2 = 0 + -1x + x + x2 + -1x2
32 + 3x + -1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
32 + 3x + -1x2 = 0 + x2 + -1x2
32 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
32 + 3x + -1x2 = 0

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

Divide each side by '-1'.
-32 + -3x + x2 = 0

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -3x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + -3x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -3x + x2 = 0 + 32
-3x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
-3x + x2 = 32

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 = 32 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 32 + 2.25

Combine like terms: 32 + 2.25 = 34.25
2.25 + -3x + x2 = 34.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(x + -1.5) equal to 5.852349955 and -5.852349955.

Subproblem 1
x + -1.5 = 5.852349955

Simplifying
x + -1.5 = 5.852349955

Reorder the terms:
-1.5 + x = 5.852349955

Solving
-1.5 + x = 5.852349955

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 = 5.852349955 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 5.852349955 + 1.5
x = 5.852349955 + 1.5

Combine like terms: 5.852349955 + 1.5 = 7.352349955
x = 7.352349955

Simplifying
x = 7.352349955

Subproblem 2
x + -1.5 = -5.852349955

Simplifying
x + -1.5 = -5.852349955

Reorder the terms:
-1.5 + x = -5.852349955

Solving
-1.5 + x = -5.852349955

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 = -5.852349955 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -5.852349955 + 1.5
x = -5.852349955 + 1.5

Combine like terms: -5.852349955 + 1.5 = -4.352349955
x = -4.352349955

Simplifying
x = -4.352349955

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.352349955, -4.352349955}