(x-3)2=(x+9)(x-9)

Solution for (x-3)2=(x+9)(x-9) equation:

Simplifying
(x + -3) * 2 = (x + 9)(x + -9)

Reorder the terms:
(-3 + x) * 2 = (x + 9)(x + -9)

Reorder the terms for easier multiplication:
2(-3 + x) = (x + 9)(x + -9)
(-3 * 2 + x * 2) = (x + 9)(x + -9)
(-6 + 2x) = (x + 9)(x + -9)

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

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

Multiply (9 + x) * (-9 + x)
-6 + 2x = (9(-9 + x) + x(-9 + x))
-6 + 2x = ((-9 * 9 + x * 9) + x(-9 + x))
-6 + 2x = ((-81 + 9x) + x(-9 + x))
-6 + 2x = (-81 + 9x + (-9 * x + x * x))
-6 + 2x = (-81 + 9x + (-9x + x2))

Combine like terms: 9x + -9x = 0
-6 + 2x = (-81 + 0 + x2)
-6 + 2x = (-81 + x2)

Solving
-6 + 2x = -81 + x2

Solving for variable 'x'.

Reorder the terms:
-6 + 81 + 2x + -1x2 = -81 + x2 + 81 + -1x2

Combine like terms: -6 + 81 = 75
75 + 2x + -1x2 = -81 + x2 + 81 + -1x2

Reorder the terms:
75 + 2x + -1x2 = -81 + 81 + x2 + -1x2

Combine like terms: -81 + 81 = 0
75 + 2x + -1x2 = 0 + x2 + -1x2
75 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
75 + 2x + -1x2 = 0

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

Divide each side by '-1'.
-75 + -2x + x2 = 0

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + -2x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + -2x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + -2x + x2 = 0 + 75
-2x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
-2x + x2 = 75

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 = 75 + 1

Reorder the terms:
1 + -2x + x2 = 75 + 1

Combine like terms: 75 + 1 = 76
1 + -2x + x2 = 76

Factor a perfect square on the left side:
(x + -1)(x + -1) = 76

Calculate the square root of the right side: 8.717797887

Break this problem into two subproblems by setting 
(x + -1) equal to 8.717797887 and -8.717797887.

Subproblem 1
x + -1 = 8.717797887

Simplifying
x + -1 = 8.717797887

Reorder the terms:
-1 + x = 8.717797887

Solving
-1 + x = 8.717797887

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 = 8.717797887 + 1

Combine like terms: -1 + 1 = 0
0 + x = 8.717797887 + 1
x = 8.717797887 + 1

Combine like terms: 8.717797887 + 1 = 9.717797887
x = 9.717797887

Simplifying
x = 9.717797887

Subproblem 2
x + -1 = -8.717797887

Simplifying
x + -1 = -8.717797887

Reorder the terms:
-1 + x = -8.717797887

Solving
-1 + x = -8.717797887

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 = -8.717797887 + 1

Combine like terms: -1 + 1 = 0
0 + x = -8.717797887 + 1
x = -8.717797887 + 1

Combine like terms: -8.717797887 + 1 = -7.717797887
x = -7.717797887

Simplifying
x = -7.717797887

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.717797887, -7.717797887}