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

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

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

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

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

Multiply (-1 + 2x) * (-3 + x)
(-1(-3 + x) + 2x * (-3 + x)) = (x + 5)(x + -1)
((-3 * -1 + x * -1) + 2x * (-3 + x)) = (x + 5)(x + -1)
((3 + -1x) + 2x * (-3 + x)) = (x + 5)(x + -1)
(3 + -1x + (-3 * 2x + x * 2x)) = (x + 5)(x + -1)
(3 + -1x + (-6x + 2x2)) = (x + 5)(x + -1)

Combine like terms: -1x + -6x = -7x
(3 + -7x + 2x2) = (x + 5)(x + -1)

Reorder the terms:
3 + -7x + 2x2 = (5 + x)(x + -1)

Reorder the terms:
3 + -7x + 2x2 = (5 + x)(-1 + x)

Multiply (5 + x) * (-1 + x)
3 + -7x + 2x2 = (5(-1 + x) + x(-1 + x))
3 + -7x + 2x2 = ((-1 * 5 + x * 5) + x(-1 + x))
3 + -7x + 2x2 = ((-5 + 5x) + x(-1 + x))
3 + -7x + 2x2 = (-5 + 5x + (-1 * x + x * x))
3 + -7x + 2x2 = (-5 + 5x + (-1x + x2))

Combine like terms: 5x + -1x = 4x
3 + -7x + 2x2 = (-5 + 4x + x2)

Solving
3 + -7x + 2x2 = -5 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
3 + 5 + -7x + -4x + 2x2 + -1x2 = -5 + 4x + x2 + 5 + -4x + -1x2

Combine like terms: 3 + 5 = 8
8 + -7x + -4x + 2x2 + -1x2 = -5 + 4x + x2 + 5 + -4x + -1x2

Combine like terms: -7x + -4x = -11x
8 + -11x + 2x2 + -1x2 = -5 + 4x + x2 + 5 + -4x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
8 + -11x + 1x2 = -5 + 4x + x2 + 5 + -4x + -1x2

Reorder the terms:
8 + -11x + 1x2 = -5 + 5 + 4x + -4x + x2 + -1x2

Combine like terms: -5 + 5 = 0
8 + -11x + 1x2 = 0 + 4x + -4x + x2 + -1x2
8 + -11x + 1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
8 + -11x + 1x2 = 0 + x2 + -1x2
8 + -11x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + -11x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -11x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -11x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -11x + x2 = 0 + -8
-11x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-11x + x2 = -8

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -8 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -8 + 30.25

Combine like terms: -8 + 30.25 = 22.25
30.25 + -11x + x2 = 22.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + -5.5) equal to 4.716990566 and -4.716990566.

Subproblem 1
x + -5.5 = 4.716990566

Simplifying
x + -5.5 = 4.716990566

Reorder the terms:
-5.5 + x = 4.716990566

Solving
-5.5 + x = 4.716990566

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 4.716990566 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 4.716990566 + 5.5
x = 4.716990566 + 5.5

Combine like terms: 4.716990566 + 5.5 = 10.216990566
x = 10.216990566

Simplifying
x = 10.216990566

Subproblem 2
x + -5.5 = -4.716990566

Simplifying
x + -5.5 = -4.716990566

Reorder the terms:
-5.5 + x = -4.716990566

Solving
-5.5 + x = -4.716990566

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -4.716990566 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -4.716990566 + 5.5
x = -4.716990566 + 5.5

Combine like terms: -4.716990566 + 5.5 = 0.783009434
x = 0.783009434

Simplifying
x = 0.783009434

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.216990566, 0.783009434}