(2x-2)2=(3x-2)(x-3)

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

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

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

Reorder the terms for easier multiplication:
2(-2 + 2x) = (3x + -2)(x + -3)
(-2 * 2 + 2x * 2) = (3x + -2)(x + -3)
(-4 + 4x) = (3x + -2)(x + -3)

Reorder the terms:
-4 + 4x = (-2 + 3x)(x + -3)

Reorder the terms:
-4 + 4x = (-2 + 3x)(-3 + x)

Multiply (-2 + 3x) * (-3 + x)
-4 + 4x = (-2(-3 + x) + 3x * (-3 + x))
-4 + 4x = ((-3 * -2 + x * -2) + 3x * (-3 + x))
-4 + 4x = ((6 + -2x) + 3x * (-3 + x))
-4 + 4x = (6 + -2x + (-3 * 3x + x * 3x))
-4 + 4x = (6 + -2x + (-9x + 3x2))

Combine like terms: -2x + -9x = -11x
-4 + 4x = (6 + -11x + 3x2)

Solving
-4 + 4x = 6 + -11x + 3x2

Solving for variable 'x'.

Reorder the terms:
-4 + -6 + 4x + 11x + -3x2 = 6 + -11x + 3x2 + -6 + 11x + -3x2

Combine like terms: -4 + -6 = -10
-10 + 4x + 11x + -3x2 = 6 + -11x + 3x2 + -6 + 11x + -3x2

Combine like terms: 4x + 11x = 15x
-10 + 15x + -3x2 = 6 + -11x + 3x2 + -6 + 11x + -3x2

Reorder the terms:
-10 + 15x + -3x2 = 6 + -6 + -11x + 11x + 3x2 + -3x2

Combine like terms: 6 + -6 = 0
-10 + 15x + -3x2 = 0 + -11x + 11x + 3x2 + -3x2
-10 + 15x + -3x2 = -11x + 11x + 3x2 + -3x2

Combine like terms: -11x + 11x = 0
-10 + 15x + -3x2 = 0 + 3x2 + -3x2
-10 + 15x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-10 + 15x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
3.333333333 + -5x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -5x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -5x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -5x + x2 = 0 + -3.333333333
-5x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-5x + x2 = -3.333333333

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -3.333333333 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -3.333333333 + 6.25

Combine like terms: -3.333333333 + 6.25 = 2.916666667
6.25 + -5x + x2 = 2.916666667

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 2.916666667

Calculate the square root of the right side: 1.707825128

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.707825128 and -1.707825128.

Subproblem 1
x + -2.5 = 1.707825128

Simplifying
x + -2.5 = 1.707825128

Reorder the terms:
-2.5 + x = 1.707825128

Solving
-2.5 + x = 1.707825128

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 1.707825128 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1.707825128 + 2.5
x = 1.707825128 + 2.5

Combine like terms: 1.707825128 + 2.5 = 4.207825128
x = 4.207825128

Simplifying
x = 4.207825128

Subproblem 2
x + -2.5 = -1.707825128

Simplifying
x + -2.5 = -1.707825128

Reorder the terms:
-2.5 + x = -1.707825128

Solving
-2.5 + x = -1.707825128

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -1.707825128 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1.707825128 + 2.5
x = -1.707825128 + 2.5

Combine like terms: -1.707825128 + 2.5 = 0.792174872
x = 0.792174872

Simplifying
x = 0.792174872

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.207825128, 0.792174872}