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

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

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

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

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

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

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

Multiply (6 + x) * (-6 + x)
-6 + 2x = (6(-6 + x) + x(-6 + x))
-6 + 2x = ((-6 * 6 + x * 6) + x(-6 + x))
-6 + 2x = ((-36 + 6x) + x(-6 + x))
-6 + 2x = (-36 + 6x + (-6 * x + x * x))
-6 + 2x = (-36 + 6x + (-6x + x2))

Combine like terms: 6x + -6x = 0
-6 + 2x = (-36 + 0 + x2)
-6 + 2x = (-36 + x2)

Solving
-6 + 2x = -36 + x2

Solving for variable 'x'.

Reorder the terms:
-6 + 36 + 2x + -1x2 = -36 + x2 + 36 + -1x2

Combine like terms: -6 + 36 = 30
30 + 2x + -1x2 = -36 + x2 + 36 + -1x2

Reorder the terms:
30 + 2x + -1x2 = -36 + 36 + x2 + -1x2

Combine like terms: -36 + 36 = 0
30 + 2x + -1x2 = 0 + x2 + -1x2
30 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
30 + 2x + -1x2 = 0

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

Divide each side by '-1'.
-30 + -2x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -2x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -2x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -2x + x2 = 0 + 30
-2x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-2x + x2 = 30

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 = 30 + 1

Reorder the terms:
1 + -2x + x2 = 30 + 1

Combine like terms: 30 + 1 = 31
1 + -2x + x2 = 31

Factor a perfect square on the left side:
(x + -1)(x + -1) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(x + -1) equal to 5.567764363 and -5.567764363.

Subproblem 1
x + -1 = 5.567764363

Simplifying
x + -1 = 5.567764363

Reorder the terms:
-1 + x = 5.567764363

Solving
-1 + x = 5.567764363

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 = 5.567764363 + 1

Combine like terms: -1 + 1 = 0
0 + x = 5.567764363 + 1
x = 5.567764363 + 1

Combine like terms: 5.567764363 + 1 = 6.567764363
x = 6.567764363

Simplifying
x = 6.567764363

Subproblem 2
x + -1 = -5.567764363

Simplifying
x + -1 = -5.567764363

Reorder the terms:
-1 + x = -5.567764363

Solving
-1 + x = -5.567764363

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 = -5.567764363 + 1

Combine like terms: -1 + 1 = 0
0 + x = -5.567764363 + 1
x = -5.567764363 + 1

Combine like terms: -5.567764363 + 1 = -4.567764363
x = -4.567764363

Simplifying
x = -4.567764363

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.567764363, -4.567764363}