(x+3)(x-3)=(x+6)2

Solution for (x+3)(x-3)=(x+6)2 equation:

Simplifying
(x + 3)(x + -3) = (x + 6) * 2

Reorder the terms:
(3 + x)(x + -3) = (x + 6) * 2

Reorder the terms:
(3 + x)(-3 + x) = (x + 6) * 2

Multiply (3 + x) * (-3 + x)
(3(-3 + x) + x(-3 + x)) = (x + 6) * 2
((-3 * 3 + x * 3) + x(-3 + x)) = (x + 6) * 2
((-9 + 3x) + x(-3 + x)) = (x + 6) * 2
(-9 + 3x + (-3 * x + x * x)) = (x + 6) * 2
(-9 + 3x + (-3x + x2)) = (x + 6) * 2

Combine like terms: 3x + -3x = 0
(-9 + 0 + x2) = (x + 6) * 2
(-9 + x2) = (x + 6) * 2

Reorder the terms:
-9 + x2 = (6 + x) * 2

Reorder the terms for easier multiplication:
-9 + x2 = 2(6 + x)
-9 + x2 = (6 * 2 + x * 2)
-9 + x2 = (12 + 2x)

Solving
-9 + x2 = 12 + 2x

Solving for variable 'x'.

Reorder the terms:
-9 + -12 + -2x + x2 = 12 + 2x + -12 + -2x

Combine like terms: -9 + -12 = -21
-21 + -2x + x2 = 12 + 2x + -12 + -2x

Reorder the terms:
-21 + -2x + x2 = 12 + -12 + 2x + -2x

Combine like terms: 12 + -12 = 0
-21 + -2x + x2 = 0 + 2x + -2x
-21 + -2x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-21 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -2x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + -2x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -2x + x2 = 0 + 21
-2x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
-2x + x2 = 21

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 = 21 + 1

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

Combine like terms: 21 + 1 = 22
1 + -2x + x2 = 22

Factor a perfect square on the left side:
(x + -1)(x + -1) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(x + -1) equal to 4.69041576 and -4.69041576.

Subproblem 1
x + -1 = 4.69041576

Simplifying
x + -1 = 4.69041576

Reorder the terms:
-1 + x = 4.69041576

Solving
-1 + x = 4.69041576

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 = 4.69041576 + 1

Combine like terms: -1 + 1 = 0
0 + x = 4.69041576 + 1
x = 4.69041576 + 1

Combine like terms: 4.69041576 + 1 = 5.69041576
x = 5.69041576

Simplifying
x = 5.69041576

Subproblem 2
x + -1 = -4.69041576

Simplifying
x + -1 = -4.69041576

Reorder the terms:
-1 + x = -4.69041576

Solving
-1 + x = -4.69041576

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 = -4.69041576 + 1

Combine like terms: -1 + 1 = 0
0 + x = -4.69041576 + 1
x = -4.69041576 + 1

Combine like terms: -4.69041576 + 1 = -3.69041576
x = -3.69041576

Simplifying
x = -3.69041576

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.69041576, -3.69041576}