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

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

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

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

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

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

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

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

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

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

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

Multiply 2 * 2
-3 + -7x + 2x2 = 4(-1 + x)
-3 + -7x + 2x2 = (-1 * 4 + x * 4)
-3 + -7x + 2x2 = (-4 + 4x)

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

Solving for variable 'x'.

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

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

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

Reorder the terms:
1 + -11x + 2x2 = -4 + 4 + 4x + -4x

Combine like terms: -4 + 4 = 0
1 + -11x + 2x2 = 0 + 4x + -4x
1 + -11x + 2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
1 + -11x + 2x2 = 0

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

Divide each side by '2'.
0.5 + -5.5x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -5.5x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -5.5x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -5.5x + x2 = 0 + -0.5
-5.5x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-5.5x + x2 = -0.5

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 = -0.5 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = -0.5 + 7.5625

Combine like terms: -0.5 + 7.5625 = 7.0625
7.5625 + -5.5x + x2 = 7.0625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 7.0625

Calculate the square root of the right side: 2.657536453

Break this problem into two subproblems by setting 
(x + -2.75) equal to 2.657536453 and -2.657536453.

Subproblem 1
x + -2.75 = 2.657536453

Simplifying
x + -2.75 = 2.657536453

Reorder the terms:
-2.75 + x = 2.657536453

Solving
-2.75 + x = 2.657536453

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 = 2.657536453 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 2.657536453 + 2.75
x = 2.657536453 + 2.75

Combine like terms: 2.657536453 + 2.75 = 5.407536453
x = 5.407536453

Simplifying
x = 5.407536453

Subproblem 2
x + -2.75 = -2.657536453

Simplifying
x + -2.75 = -2.657536453

Reorder the terms:
-2.75 + x = -2.657536453

Solving
-2.75 + x = -2.657536453

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 = -2.657536453 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -2.657536453 + 2.75
x = -2.657536453 + 2.75

Combine like terms: -2.657536453 + 2.75 = 0.092463547
x = 0.092463547

Simplifying
x = 0.092463547

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.407536453, 0.092463547}