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

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

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

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

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

Multiply (-4 + x) * (1 + 5x)
(-4(1 + 5x) + x(1 + 5x)) = (2x + 5)(2x + -2)
((1 * -4 + 5x * -4) + x(1 + 5x)) = (2x + 5)(2x + -2)
((-4 + -20x) + x(1 + 5x)) = (2x + 5)(2x + -2)
(-4 + -20x + (1 * x + 5x * x)) = (2x + 5)(2x + -2)
(-4 + -20x + (1x + 5x2)) = (2x + 5)(2x + -2)

Combine like terms: -20x + 1x = -19x
(-4 + -19x + 5x2) = (2x + 5)(2x + -2)

Reorder the terms:
-4 + -19x + 5x2 = (5 + 2x)(2x + -2)

Reorder the terms:
-4 + -19x + 5x2 = (5 + 2x)(-2 + 2x)

Multiply (5 + 2x) * (-2 + 2x)
-4 + -19x + 5x2 = (5(-2 + 2x) + 2x * (-2 + 2x))
-4 + -19x + 5x2 = ((-2 * 5 + 2x * 5) + 2x * (-2 + 2x))
-4 + -19x + 5x2 = ((-10 + 10x) + 2x * (-2 + 2x))
-4 + -19x + 5x2 = (-10 + 10x + (-2 * 2x + 2x * 2x))
-4 + -19x + 5x2 = (-10 + 10x + (-4x + 4x2))

Combine like terms: 10x + -4x = 6x
-4 + -19x + 5x2 = (-10 + 6x + 4x2)

Solving
-4 + -19x + 5x2 = -10 + 6x + 4x2

Solving for variable 'x'.

Reorder the terms:
-4 + 10 + -19x + -6x + 5x2 + -4x2 = -10 + 6x + 4x2 + 10 + -6x + -4x2

Combine like terms: -4 + 10 = 6
6 + -19x + -6x + 5x2 + -4x2 = -10 + 6x + 4x2 + 10 + -6x + -4x2

Combine like terms: -19x + -6x = -25x
6 + -25x + 5x2 + -4x2 = -10 + 6x + 4x2 + 10 + -6x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
6 + -25x + 1x2 = -10 + 6x + 4x2 + 10 + -6x + -4x2

Reorder the terms:
6 + -25x + 1x2 = -10 + 10 + 6x + -6x + 4x2 + -4x2

Combine like terms: -10 + 10 = 0
6 + -25x + 1x2 = 0 + 6x + -6x + 4x2 + -4x2
6 + -25x + 1x2 = 6x + -6x + 4x2 + -4x2

Combine like terms: 6x + -6x = 0
6 + -25x + 1x2 = 0 + 4x2 + -4x2
6 + -25x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
6 + -25x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -25x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -25x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -25x + x2 = 0 + -6
-25x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-25x + x2 = -6

The x term is -25x.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25x + 156.25 + x2 = -6 + 156.25

Reorder the terms:
156.25 + -25x + x2 = -6 + 156.25

Combine like terms: -6 + 156.25 = 150.25
156.25 + -25x + x2 = 150.25

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 150.25

Calculate the square root of the right side: 12.257650672

Break this problem into two subproblems by setting 
(x + -12.5) equal to 12.257650672 and -12.257650672.

Subproblem 1
x + -12.5 = 12.257650672

Simplifying
x + -12.5 = 12.257650672

Reorder the terms:
-12.5 + x = 12.257650672

Solving
-12.5 + x = 12.257650672

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = 12.257650672 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = 12.257650672 + 12.5
x = 12.257650672 + 12.5

Combine like terms: 12.257650672 + 12.5 = 24.757650672
x = 24.757650672

Simplifying
x = 24.757650672

Subproblem 2
x + -12.5 = -12.257650672

Simplifying
x + -12.5 = -12.257650672

Reorder the terms:
-12.5 + x = -12.257650672

Solving
-12.5 + x = -12.257650672

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = -12.257650672 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = -12.257650672 + 12.5
x = -12.257650672 + 12.5

Combine like terms: -12.257650672 + 12.5 = 0.242349328
x = 0.242349328

Simplifying
x = 0.242349328

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.757650672, 0.242349328}