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

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

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

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

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

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

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

Multiply (4 + x) * (-4 + x)
6 + 2x + -1(4(-4 + x) + x(-4 + x)) = x + -2
6 + 2x + -1((-4 * 4 + x * 4) + x(-4 + x)) = x + -2
6 + 2x + -1((-16 + 4x) + x(-4 + x)) = x + -2
6 + 2x + -1(-16 + 4x + (-4 * x + x * x)) = x + -2
6 + 2x + -1(-16 + 4x + (-4x + x2)) = x + -2

Combine like terms: 4x + -4x = 0
6 + 2x + -1(-16 + 0 + x2) = x + -2
6 + 2x + -1(-16 + x2) = x + -2
6 + 2x + (-16 * -1 + x2 * -1) = x + -2
6 + 2x + (16 + -1x2) = x + -2

Reorder the terms:
6 + 16 + 2x + -1x2 = x + -2

Combine like terms: 6 + 16 = 22
22 + 2x + -1x2 = x + -2

Reorder the terms:
22 + 2x + -1x2 = -2 + x

Solving
22 + 2x + -1x2 = -2 + x

Solving for variable 'x'.

Reorder the terms:
22 + 2 + 2x + -1x + -1x2 = -2 + x + 2 + -1x

Combine like terms: 22 + 2 = 24
24 + 2x + -1x + -1x2 = -2 + x + 2 + -1x

Combine like terms: 2x + -1x = 1x
24 + 1x + -1x2 = -2 + x + 2 + -1x

Reorder the terms:
24 + 1x + -1x2 = -2 + 2 + x + -1x

Combine like terms: -2 + 2 = 0
24 + 1x + -1x2 = 0 + x + -1x
24 + 1x + -1x2 = x + -1x

Combine like terms: x + -1x = 0
24 + 1x + -1x2 = 0

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

Divide each side by '-1'.
-24 + -1x + x2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -1x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + -1x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1x + x2 = 0 + 24
-1x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
-1x + x2 = 24

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 = 24 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 24 + 0.25

Combine like terms: 24 + 0.25 = 24.25
0.25 + -1x + x2 = 24.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + -0.5) equal to 4.924428901 and -4.924428901.

Subproblem 1
x + -0.5 = 4.924428901

Simplifying
x + -0.5 = 4.924428901

Reorder the terms:
-0.5 + x = 4.924428901

Solving
-0.5 + x = 4.924428901

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 = 4.924428901 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 4.924428901 + 0.5
x = 4.924428901 + 0.5

Combine like terms: 4.924428901 + 0.5 = 5.424428901
x = 5.424428901

Simplifying
x = 5.424428901

Subproblem 2
x + -0.5 = -4.924428901

Simplifying
x + -0.5 = -4.924428901

Reorder the terms:
-0.5 + x = -4.924428901

Solving
-0.5 + x = -4.924428901

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 = -4.924428901 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -4.924428901 + 0.5
x = -4.924428901 + 0.5

Combine like terms: -4.924428901 + 0.5 = -4.424428901
x = -4.424428901

Simplifying
x = -4.424428901

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.424428901, -4.424428901}