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

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

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

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

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

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

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

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

Remove parenthesis around (6 + x)
-9 + x2 = 6 + x

Solving
-9 + x2 = 6 + x

Solving for variable 'x'.

Reorder the terms:
-9 + -6 + -1x + x2 = 6 + x + -6 + -1x

Combine like terms: -9 + -6 = -15
-15 + -1x + x2 = 6 + x + -6 + -1x

Reorder the terms:
-15 + -1x + x2 = 6 + -6 + x + -1x

Combine like terms: 6 + -6 = 0
-15 + -1x + x2 = 0 + x + -1x
-15 + -1x + x2 = x + -1x

Combine like terms: x + -1x = 0
-15 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -1x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -1x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x + x2 = 0 + 15
-1x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-1x + x2 = 15

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 = 15 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 15 + 0.25

Combine like terms: 15 + 0.25 = 15.25
0.25 + -1x + x2 = 15.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + -0.5) equal to 3.905124838 and -3.905124838.

Subproblem 1
x + -0.5 = 3.905124838

Simplifying
x + -0.5 = 3.905124838

Reorder the terms:
-0.5 + x = 3.905124838

Solving
-0.5 + x = 3.905124838

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 = 3.905124838 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 3.905124838 + 0.5
x = 3.905124838 + 0.5

Combine like terms: 3.905124838 + 0.5 = 4.405124838
x = 4.405124838

Simplifying
x = 4.405124838

Subproblem 2
x + -0.5 = -3.905124838

Simplifying
x + -0.5 = -3.905124838

Reorder the terms:
-0.5 + x = -3.905124838

Solving
-0.5 + x = -3.905124838

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 = -3.905124838 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -3.905124838 + 0.5
x = -3.905124838 + 0.5

Combine like terms: -3.905124838 + 0.5 = -3.405124838
x = -3.405124838

Simplifying
x = -3.405124838

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.405124838, -3.405124838}