5(x-3)2(x-3)-9=0

Solution for 5(x-3)2(x-3)-9=0 equation:

Simplifying
5(x + -3) * 2(x + -3) + -9 = 0

Reorder the terms:
5(-3 + x) * 2(x + -3) + -9 = 0

Reorder the terms:
5(-3 + x) * 2(-3 + x) + -9 = 0

Reorder the terms for easier multiplication:
5 * 2(-3 + x)(-3 + x) + -9 = 0

Multiply 5 * 2
10(-3 + x)(-3 + x) + -9 = 0

Multiply (-3 + x) * (-3 + x)
10(-3(-3 + x) + x(-3 + x)) + -9 = 0
10((-3 * -3 + x * -3) + x(-3 + x)) + -9 = 0
10((9 + -3x) + x(-3 + x)) + -9 = 0
10(9 + -3x + (-3 * x + x * x)) + -9 = 0
10(9 + -3x + (-3x + x2)) + -9 = 0

Combine like terms: -3x + -3x = -6x
10(9 + -6x + x2) + -9 = 0
(9 * 10 + -6x * 10 + x2 * 10) + -9 = 0
(90 + -60x + 10x2) + -9 = 0

Reorder the terms:
90 + -9 + -60x + 10x2 = 0

Combine like terms: 90 + -9 = 81
81 + -60x + 10x2 = 0

Solving
81 + -60x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
8.1 + -6x + x2 = 0.0

Move the constant term to the right:

Add '-8.1' to each side of the equation.
8.1 + -6x + -8.1 + x2 = 0.0 + -8.1

Reorder the terms:
8.1 + -8.1 + -6x + x2 = 0.0 + -8.1

Combine like terms: 8.1 + -8.1 = 0.0
0.0 + -6x + x2 = 0.0 + -8.1
-6x + x2 = 0.0 + -8.1

Combine like terms: 0.0 + -8.1 = -8.1
-6x + x2 = -8.1

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -8.1 + 9

Reorder the terms:
9 + -6x + x2 = -8.1 + 9

Combine like terms: -8.1 + 9 = 0.9
9 + -6x + x2 = 0.9

Factor a perfect square on the left side:
(x + -3)(x + -3) = 0.9

Calculate the square root of the right side: 0.948683298

Break this problem into two subproblems by setting 
(x + -3) equal to 0.948683298 and -0.948683298.

Subproblem 1
x + -3 = 0.948683298

Simplifying
x + -3 = 0.948683298

Reorder the terms:
-3 + x = 0.948683298

Solving
-3 + x = 0.948683298

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 0.948683298 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0.948683298 + 3
x = 0.948683298 + 3

Combine like terms: 0.948683298 + 3 = 3.948683298
x = 3.948683298

Simplifying
x = 3.948683298

Subproblem 2
x + -3 = -0.948683298

Simplifying
x + -3 = -0.948683298

Reorder the terms:
-3 + x = -0.948683298

Solving
-3 + x = -0.948683298

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -0.948683298 + 3

Combine like terms: -3 + 3 = 0
0 + x = -0.948683298 + 3
x = -0.948683298 + 3

Combine like terms: -0.948683298 + 3 = 2.051316702
x = 2.051316702

Simplifying
x = 2.051316702

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.948683298, 2.051316702}