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

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

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

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

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

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

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

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

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

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

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

Solving for variable 'x'.

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

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

Combine like terms: -7x + -2x = -9x
-1 + -9x + 2x2 = -2 + 2x + 2 + -2x

Reorder the terms:
-1 + -9x + 2x2 = -2 + 2 + 2x + -2x

Combine like terms: -2 + 2 = 0
-1 + -9x + 2x2 = 0 + 2x + -2x
-1 + -9x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-1 + -9x + 2x2 = 0

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

Divide each side by '2'.
-0.5 + -4.5x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -4.5x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -4.5x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -4.5x + x2 = 0 + 0.5
-4.5x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-4.5x + x2 = 0.5

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 0.5 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 0.5 + 5.0625

Combine like terms: 0.5 + 5.0625 = 5.5625
5.0625 + -4.5x + x2 = 5.5625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(x + -2.25) equal to 2.358495283 and -2.358495283.

Subproblem 1
x + -2.25 = 2.358495283

Simplifying
x + -2.25 = 2.358495283

Reorder the terms:
-2.25 + x = 2.358495283

Solving
-2.25 + x = 2.358495283

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 2.358495283 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 2.358495283 + 2.25
x = 2.358495283 + 2.25

Combine like terms: 2.358495283 + 2.25 = 4.608495283
x = 4.608495283

Simplifying
x = 4.608495283

Subproblem 2
x + -2.25 = -2.358495283

Simplifying
x + -2.25 = -2.358495283

Reorder the terms:
-2.25 + x = -2.358495283

Solving
-2.25 + x = -2.358495283

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -2.358495283 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -2.358495283 + 2.25
x = -2.358495283 + 2.25

Combine like terms: -2.358495283 + 2.25 = -0.108495283
x = -0.108495283

Simplifying
x = -0.108495283

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.608495283, -0.108495283}