(2x-5)2=4(x-3)(x-1)

Solution for (2x-5)2=4(x-3)(x-1) equation:

Simplifying
(2x + -5) * 2 = 4(x + -3)(x + -1)

Reorder the terms:
(-5 + 2x) * 2 = 4(x + -3)(x + -1)

Reorder the terms for easier multiplication:
2(-5 + 2x) = 4(x + -3)(x + -1)
(-5 * 2 + 2x * 2) = 4(x + -3)(x + -1)
(-10 + 4x) = 4(x + -3)(x + -1)

Reorder the terms:
-10 + 4x = 4(-3 + x)(x + -1)

Reorder the terms:
-10 + 4x = 4(-3 + x)(-1 + x)

Multiply (-3 + x) * (-1 + x)
-10 + 4x = 4(-3(-1 + x) + x(-1 + x))
-10 + 4x = 4((-1 * -3 + x * -3) + x(-1 + x))
-10 + 4x = 4((3 + -3x) + x(-1 + x))
-10 + 4x = 4(3 + -3x + (-1 * x + x * x))
-10 + 4x = 4(3 + -3x + (-1x + x2))

Combine like terms: -3x + -1x = -4x
-10 + 4x = 4(3 + -4x + x2)
-10 + 4x = (3 * 4 + -4x * 4 + x2 * 4)
-10 + 4x = (12 + -16x + 4x2)

Solving
-10 + 4x = 12 + -16x + 4x2

Solving for variable 'x'.

Reorder the terms:
-10 + -12 + 4x + 16x + -4x2 = 12 + -16x + 4x2 + -12 + 16x + -4x2

Combine like terms: -10 + -12 = -22
-22 + 4x + 16x + -4x2 = 12 + -16x + 4x2 + -12 + 16x + -4x2

Combine like terms: 4x + 16x = 20x
-22 + 20x + -4x2 = 12 + -16x + 4x2 + -12 + 16x + -4x2

Reorder the terms:
-22 + 20x + -4x2 = 12 + -12 + -16x + 16x + 4x2 + -4x2

Combine like terms: 12 + -12 = 0
-22 + 20x + -4x2 = 0 + -16x + 16x + 4x2 + -4x2
-22 + 20x + -4x2 = -16x + 16x + 4x2 + -4x2

Combine like terms: -16x + 16x = 0
-22 + 20x + -4x2 = 0 + 4x2 + -4x2
-22 + 20x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-22 + 20x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + 10x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-11 + 10x + -2x2)' equal to zero and attempt to solve:

Simplifying
-11 + 10x + -2x2 = 0

Solving
-11 + 10x + -2x2 = 0

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

Divide each side by '-2'.
5.5 + -5x + x2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + -5x + -5.5 + x2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + -5x + x2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + -5x + x2 = 0 + -5.5
-5x + x2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
-5x + x2 = -5.5

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 = -5.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -5.5 + 6.25

Combine like terms: -5.5 + 6.25 = 0.75
6.25 + -5x + x2 = 0.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(x + -2.5) equal to 0.866025404 and -0.866025404.

Subproblem 1
x + -2.5 = 0.866025404

Simplifying
x + -2.5 = 0.866025404

Reorder the terms:
-2.5 + x = 0.866025404

Solving
-2.5 + x = 0.866025404

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 = 0.866025404 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 0.866025404 + 2.5
x = 0.866025404 + 2.5

Combine like terms: 0.866025404 + 2.5 = 3.366025404
x = 3.366025404

Simplifying
x = 3.366025404

Subproblem 2
x + -2.5 = -0.866025404

Simplifying
x + -2.5 = -0.866025404

Reorder the terms:
-2.5 + x = -0.866025404

Solving
-2.5 + x = -0.866025404

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 = -0.866025404 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -0.866025404 + 2.5
x = -0.866025404 + 2.5

Combine like terms: -0.866025404 + 2.5 = 1.633974596
x = 1.633974596

Simplifying
x = 1.633974596

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.366025404, 1.633974596}
Solution
x = {3.366025404, 1.633974596}