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

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

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

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

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

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

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

Multiply (-3 + x) * (6 + 3x)
(-3(6 + 3x) + x(6 + 3x)) = 9(9 + 2x + 2)
((6 * -3 + 3x * -3) + x(6 + 3x)) = 9(9 + 2x + 2)
((-18 + -9x) + x(6 + 3x)) = 9(9 + 2x + 2)
(-18 + -9x + (6 * x + 3x * x)) = 9(9 + 2x + 2)
(-18 + -9x + (6x + 3x2)) = 9(9 + 2x + 2)

Combine like terms: -9x + 6x = -3x
(-18 + -3x + 3x2) = 9(9 + 2x + 2)

Reorder the terms:
-18 + -3x + 3x2 = 9(9 + 2 + 2x)

Combine like terms: 9 + 2 = 11
-18 + -3x + 3x2 = 9(11 + 2x)
-18 + -3x + 3x2 = (11 * 9 + 2x * 9)
-18 + -3x + 3x2 = (99 + 18x)

Solving
-18 + -3x + 3x2 = 99 + 18x

Solving for variable 'x'.

Reorder the terms:
-18 + -99 + -3x + -18x + 3x2 = 99 + 18x + -99 + -18x

Combine like terms: -18 + -99 = -117
-117 + -3x + -18x + 3x2 = 99 + 18x + -99 + -18x

Combine like terms: -3x + -18x = -21x
-117 + -21x + 3x2 = 99 + 18x + -99 + -18x

Reorder the terms:
-117 + -21x + 3x2 = 99 + -99 + 18x + -18x

Combine like terms: 99 + -99 = 0
-117 + -21x + 3x2 = 0 + 18x + -18x
-117 + -21x + 3x2 = 18x + -18x

Combine like terms: 18x + -18x = 0
-117 + -21x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-39 + -7x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-39 + -7x + x2)' equal to zero and attempt to solve:

Simplifying
-39 + -7x + x2 = 0

Solving
-39 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + -7x + 39 + x2 = 0 + 39

Reorder the terms:
-39 + 39 + -7x + x2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + -7x + x2 = 0 + 39
-7x + x2 = 0 + 39

Combine like terms: 0 + 39 = 39
-7x + x2 = 39

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 39 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 39 + 12.25

Combine like terms: 39 + 12.25 = 51.25
12.25 + -7x + x2 = 51.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 51.25

Calculate the square root of the right side: 7.158910532

Break this problem into two subproblems by setting 
(x + -3.5) equal to 7.158910532 and -7.158910532.

Subproblem 1
x + -3.5 = 7.158910532

Simplifying
x + -3.5 = 7.158910532

Reorder the terms:
-3.5 + x = 7.158910532

Solving
-3.5 + x = 7.158910532

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 7.158910532 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 7.158910532 + 3.5
x = 7.158910532 + 3.5

Combine like terms: 7.158910532 + 3.5 = 10.658910532
x = 10.658910532

Simplifying
x = 10.658910532

Subproblem 2
x + -3.5 = -7.158910532

Simplifying
x + -3.5 = -7.158910532

Reorder the terms:
-3.5 + x = -7.158910532

Solving
-3.5 + x = -7.158910532

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -7.158910532 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -7.158910532 + 3.5
x = -7.158910532 + 3.5

Combine like terms: -7.158910532 + 3.5 = -3.658910532
x = -3.658910532

Simplifying
x = -3.658910532

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.658910532, -3.658910532}
Solution
x = {10.658910532, -3.658910532}