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

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

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

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

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

Multiply (-4 + x) * (4 + x)
(-4(4 + x) + x(4 + x)) = (x + 5)
((4 * -4 + x * -4) + x(4 + x)) = (x + 5)
((-16 + -4x) + x(4 + x)) = (x + 5)
(-16 + -4x + (4 * x + x * x)) = (x + 5)
(-16 + -4x + (4x + x2)) = (x + 5)

Combine like terms: -4x + 4x = 0
(-16 + 0 + x2) = (x + 5)
(-16 + x2) = (x + 5)

Reorder the terms:
-16 + x2 = (5 + x)

Remove parenthesis around (5 + x)
-16 + x2 = 5 + x

Solving
-16 + x2 = 5 + x

Solving for variable 'x'.

Reorder the terms:
-16 + -5 + -1x + x2 = 5 + x + -5 + -1x

Combine like terms: -16 + -5 = -21
-21 + -1x + x2 = 5 + x + -5 + -1x

Reorder the terms:
-21 + -1x + x2 = 5 + -5 + x + -1x

Combine like terms: 5 + -5 = 0
-21 + -1x + x2 = 0 + x + -1x
-21 + -1x + x2 = x + -1x

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

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -1x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + -1x + x2 = 0 + 21

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

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

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 = 21 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 21 + 0.25

Combine like terms: 21 + 0.25 = 21.25
0.25 + -1x + x2 = 21.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(x + -0.5) equal to 4.609772229 and -4.609772229.

Subproblem 1
x + -0.5 = 4.609772229

Simplifying
x + -0.5 = 4.609772229

Reorder the terms:
-0.5 + x = 4.609772229

Solving
-0.5 + x = 4.609772229

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 = 4.609772229 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 4.609772229 + 0.5
x = 4.609772229 + 0.5

Combine like terms: 4.609772229 + 0.5 = 5.109772229
x = 5.109772229

Simplifying
x = 5.109772229

Subproblem 2
x + -0.5 = -4.609772229

Simplifying
x + -0.5 = -4.609772229

Reorder the terms:
-0.5 + x = -4.609772229

Solving
-0.5 + x = -4.609772229

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 = -4.609772229 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -4.609772229 + 0.5
x = -4.609772229 + 0.5

Combine like terms: -4.609772229 + 0.5 = -4.109772229
x = -4.109772229

Simplifying
x = -4.109772229

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.109772229, -4.109772229}