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

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

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

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

Reorder the terms:
-10 + 2x = (1 + 2x)(x + -4)

Reorder the terms:
-10 + 2x = (1 + 2x)(-4 + x)

Multiply (1 + 2x) * (-4 + x)
-10 + 2x = (1(-4 + x) + 2x * (-4 + x))
-10 + 2x = ((-4 * 1 + x * 1) + 2x * (-4 + x))
-10 + 2x = ((-4 + 1x) + 2x * (-4 + x))
-10 + 2x = (-4 + 1x + (-4 * 2x + x * 2x))
-10 + 2x = (-4 + 1x + (-8x + 2x2))

Combine like terms: 1x + -8x = -7x
-10 + 2x = (-4 + -7x + 2x2)

Solving
-10 + 2x = -4 + -7x + 2x2

Solving for variable 'x'.

Reorder the terms:
-10 + 4 + 2x + 7x + -2x2 = -4 + -7x + 2x2 + 4 + 7x + -2x2

Combine like terms: -10 + 4 = -6
-6 + 2x + 7x + -2x2 = -4 + -7x + 2x2 + 4 + 7x + -2x2

Combine like terms: 2x + 7x = 9x
-6 + 9x + -2x2 = -4 + -7x + 2x2 + 4 + 7x + -2x2

Reorder the terms:
-6 + 9x + -2x2 = -4 + 4 + -7x + 7x + 2x2 + -2x2

Combine like terms: -4 + 4 = 0
-6 + 9x + -2x2 = 0 + -7x + 7x + 2x2 + -2x2
-6 + 9x + -2x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
-6 + 9x + -2x2 = 0 + 2x2 + -2x2
-6 + 9x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-6 + 9x + -2x2 = 0

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

Divide each side by '-2'.
3 + -4.5x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -4.5x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -4.5x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4.5x + x2 = 0 + -3
-4.5x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-4.5x + x2 = -3

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 = -3 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = -3 + 5.0625

Combine like terms: -3 + 5.0625 = 2.0625
5.0625 + -4.5x + x2 = 2.0625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(x + -2.25) equal to 1.436140662 and -1.436140662.

Subproblem 1
x + -2.25 = 1.436140662

Simplifying
x + -2.25 = 1.436140662

Reorder the terms:
-2.25 + x = 1.436140662

Solving
-2.25 + x = 1.436140662

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 = 1.436140662 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 1.436140662 + 2.25
x = 1.436140662 + 2.25

Combine like terms: 1.436140662 + 2.25 = 3.686140662
x = 3.686140662

Simplifying
x = 3.686140662

Subproblem 2
x + -2.25 = -1.436140662

Simplifying
x + -2.25 = -1.436140662

Reorder the terms:
-2.25 + x = -1.436140662

Solving
-2.25 + x = -1.436140662

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 = -1.436140662 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -1.436140662 + 2.25
x = -1.436140662 + 2.25

Combine like terms: -1.436140662 + 2.25 = 0.813859338
x = 0.813859338

Simplifying
x = 0.813859338

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.686140662, 0.813859338}