2(x-2)2=(2x-1)(x-3)

Solution for 2(x-2)2=(2x-1)(x-3) equation:

Simplifying
2(x + -2) * 2 = (2x + -1)(x + -3)

Reorder the terms:
2(-2 + x) * 2 = (2x + -1)(x + -3)

Reorder the terms for easier multiplication:
2 * 2(-2 + x) = (2x + -1)(x + -3)

Multiply 2 * 2
4(-2 + x) = (2x + -1)(x + -3)
(-2 * 4 + x * 4) = (2x + -1)(x + -3)
(-8 + 4x) = (2x + -1)(x + -3)

Reorder the terms:
-8 + 4x = (-1 + 2x)(x + -3)

Reorder the terms:
-8 + 4x = (-1 + 2x)(-3 + x)

Multiply (-1 + 2x) * (-3 + x)
-8 + 4x = (-1(-3 + x) + 2x * (-3 + x))
-8 + 4x = ((-3 * -1 + x * -1) + 2x * (-3 + x))
-8 + 4x = ((3 + -1x) + 2x * (-3 + x))
-8 + 4x = (3 + -1x + (-3 * 2x + x * 2x))
-8 + 4x = (3 + -1x + (-6x + 2x2))

Combine like terms: -1x + -6x = -7x
-8 + 4x = (3 + -7x + 2x2)

Solving
-8 + 4x = 3 + -7x + 2x2

Solving for variable 'x'.

Reorder the terms:
-8 + -3 + 4x + 7x + -2x2 = 3 + -7x + 2x2 + -3 + 7x + -2x2

Combine like terms: -8 + -3 = -11
-11 + 4x + 7x + -2x2 = 3 + -7x + 2x2 + -3 + 7x + -2x2

Combine like terms: 4x + 7x = 11x
-11 + 11x + -2x2 = 3 + -7x + 2x2 + -3 + 7x + -2x2

Reorder the terms:
-11 + 11x + -2x2 = 3 + -3 + -7x + 7x + 2x2 + -2x2

Combine like terms: 3 + -3 = 0
-11 + 11x + -2x2 = 0 + -7x + 7x + 2x2 + -2x2
-11 + 11x + -2x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
-11 + 11x + -2x2 = 0 + 2x2 + -2x2
-11 + 11x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-11 + 11x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
5.5 + -5.5x + x2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + -5.5x + -5.5 + x2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + -5.5x + x2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + -5.5x + x2 = 0 + -5.5
-5.5x + x2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
-5.5x + x2 = -5.5

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = -5.5 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = -5.5 + 7.5625

Combine like terms: -5.5 + 7.5625 = 2.0625
7.5625 + -5.5x + x2 = 2.0625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(x + -2.75) equal to 1.436140662 and -1.436140662.

Subproblem 1
x + -2.75 = 1.436140662

Simplifying
x + -2.75 = 1.436140662

Reorder the terms:
-2.75 + x = 1.436140662

Solving
-2.75 + x = 1.436140662

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 1.436140662 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 1.436140662 + 2.75
x = 1.436140662 + 2.75

Combine like terms: 1.436140662 + 2.75 = 4.186140662
x = 4.186140662

Simplifying
x = 4.186140662

Subproblem 2
x + -2.75 = -1.436140662

Simplifying
x + -2.75 = -1.436140662

Reorder the terms:
-2.75 + x = -1.436140662

Solving
-2.75 + x = -1.436140662

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -1.436140662 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -1.436140662 + 2.75
x = -1.436140662 + 2.75

Combine like terms: -1.436140662 + 2.75 = 1.313859338
x = 1.313859338

Simplifying
x = 1.313859338

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.186140662, 1.313859338}