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

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

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

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

Reorder the terms for easier multiplication:
2(5 + x) = (x + -4)(x + 4)
(5 * 2 + x * 2) = (x + -4)(x + 4)
(10 + 2x) = (x + -4)(x + 4)

Reorder the terms:
10 + 2x = (-4 + x)(x + 4)

Reorder the terms:
10 + 2x = (-4 + x)(4 + x)

Multiply (-4 + x) * (4 + x)
10 + 2x = (-4(4 + x) + x(4 + x))
10 + 2x = ((4 * -4 + x * -4) + x(4 + x))
10 + 2x = ((-16 + -4x) + x(4 + x))
10 + 2x = (-16 + -4x + (4 * x + x * x))
10 + 2x = (-16 + -4x + (4x + x2))

Combine like terms: -4x + 4x = 0
10 + 2x = (-16 + 0 + x2)
10 + 2x = (-16 + x2)

Solving
10 + 2x = -16 + x2

Solving for variable 'x'.

Reorder the terms:
10 + 16 + 2x + -1x2 = -16 + x2 + 16 + -1x2

Combine like terms: 10 + 16 = 26
26 + 2x + -1x2 = -16 + x2 + 16 + -1x2

Reorder the terms:
26 + 2x + -1x2 = -16 + 16 + x2 + -1x2

Combine like terms: -16 + 16 = 0
26 + 2x + -1x2 = 0 + x2 + -1x2
26 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
26 + 2x + -1x2 = 0

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

Divide each side by '-1'.
-26 + -2x + x2 = 0

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + -2x + 26 + x2 = 0 + 26

Reorder the terms:
-26 + 26 + -2x + x2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -2x + x2 = 0 + 26
-2x + x2 = 0 + 26

Combine like terms: 0 + 26 = 26
-2x + x2 = 26

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 = 26 + 1

Reorder the terms:
1 + -2x + x2 = 26 + 1

Combine like terms: 26 + 1 = 27
1 + -2x + x2 = 27

Factor a perfect square on the left side:
(x + -1)(x + -1) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(x + -1) equal to 5.196152423 and -5.196152423.

Subproblem 1
x + -1 = 5.196152423

Simplifying
x + -1 = 5.196152423

Reorder the terms:
-1 + x = 5.196152423

Solving
-1 + x = 5.196152423

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 = 5.196152423 + 1

Combine like terms: -1 + 1 = 0
0 + x = 5.196152423 + 1
x = 5.196152423 + 1

Combine like terms: 5.196152423 + 1 = 6.196152423
x = 6.196152423

Simplifying
x = 6.196152423

Subproblem 2
x + -1 = -5.196152423

Simplifying
x + -1 = -5.196152423

Reorder the terms:
-1 + x = -5.196152423

Solving
-1 + x = -5.196152423

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 = -5.196152423 + 1

Combine like terms: -1 + 1 = 0
0 + x = -5.196152423 + 1
x = -5.196152423 + 1

Combine like terms: -5.196152423 + 1 = -4.196152423
x = -4.196152423

Simplifying
x = -4.196152423

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.196152423, -4.196152423}