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

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

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

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

Remove parenthesis around (2 + 4x)
2 + 4x + (2x + -5) = 5(2x + -5)(4x + 2)

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

Remove parenthesis around (-5 + 2x)
2 + 4x + -5 + 2x = 5(2x + -5)(4x + 2)

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

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

Combine like terms: 4x + 2x = 6x
-3 + 6x = 5(2x + -5)(4x + 2)

Reorder the terms:
-3 + 6x = 5(-5 + 2x)(4x + 2)

Reorder the terms:
-3 + 6x = 5(-5 + 2x)(2 + 4x)

Multiply (-5 + 2x) * (2 + 4x)
-3 + 6x = 5(-5(2 + 4x) + 2x * (2 + 4x))
-3 + 6x = 5((2 * -5 + 4x * -5) + 2x * (2 + 4x))
-3 + 6x = 5((-10 + -20x) + 2x * (2 + 4x))
-3 + 6x = 5(-10 + -20x + (2 * 2x + 4x * 2x))
-3 + 6x = 5(-10 + -20x + (4x + 8x2))

Combine like terms: -20x + 4x = -16x
-3 + 6x = 5(-10 + -16x + 8x2)
-3 + 6x = (-10 * 5 + -16x * 5 + 8x2 * 5)
-3 + 6x = (-50 + -80x + 40x2)

Solving
-3 + 6x = -50 + -80x + 40x2

Solving for variable 'x'.

Reorder the terms:
-3 + 50 + 6x + 80x + -40x2 = -50 + -80x + 40x2 + 50 + 80x + -40x2

Combine like terms: -3 + 50 = 47
47 + 6x + 80x + -40x2 = -50 + -80x + 40x2 + 50 + 80x + -40x2

Combine like terms: 6x + 80x = 86x
47 + 86x + -40x2 = -50 + -80x + 40x2 + 50 + 80x + -40x2

Reorder the terms:
47 + 86x + -40x2 = -50 + 50 + -80x + 80x + 40x2 + -40x2

Combine like terms: -50 + 50 = 0
47 + 86x + -40x2 = 0 + -80x + 80x + 40x2 + -40x2
47 + 86x + -40x2 = -80x + 80x + 40x2 + -40x2

Combine like terms: -80x + 80x = 0
47 + 86x + -40x2 = 0 + 40x2 + -40x2
47 + 86x + -40x2 = 40x2 + -40x2

Combine like terms: 40x2 + -40x2 = 0
47 + 86x + -40x2 = 0

Begin completing the square.  Divide all terms by
-40 the coefficient of the squared term: 

Divide each side by '-40'.
-1.175 + -2.15x + x2 = 0

Move the constant term to the right:

Add '1.175' to each side of the equation.
-1.175 + -2.15x + 1.175 + x2 = 0 + 1.175

Reorder the terms:
-1.175 + 1.175 + -2.15x + x2 = 0 + 1.175

Combine like terms: -1.175 + 1.175 = 0.000
0.000 + -2.15x + x2 = 0 + 1.175
-2.15x + x2 = 0 + 1.175

Combine like terms: 0 + 1.175 = 1.175
-2.15x + x2 = 1.175

The x term is -2.15x.  Take half its coefficient (-1.075).
Square it (1.155625) and add it to both sides.

Add '1.155625' to each side of the equation.
-2.15x + 1.155625 + x2 = 1.175 + 1.155625

Reorder the terms:
1.155625 + -2.15x + x2 = 1.175 + 1.155625

Combine like terms: 1.175 + 1.155625 = 2.330625
1.155625 + -2.15x + x2 = 2.330625

Factor a perfect square on the left side:
(x + -1.075)(x + -1.075) = 2.330625

Calculate the square root of the right side: 1.526638464

Break this problem into two subproblems by setting 
(x + -1.075) equal to 1.526638464 and -1.526638464.

Subproblem 1
x + -1.075 = 1.526638464

Simplifying
x + -1.075 = 1.526638464

Reorder the terms:
-1.075 + x = 1.526638464

Solving
-1.075 + x = 1.526638464

Solving for variable 'x'.

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

Add '1.075' to each side of the equation.
-1.075 + 1.075 + x = 1.526638464 + 1.075

Combine like terms: -1.075 + 1.075 = 0.000
0.000 + x = 1.526638464 + 1.075
x = 1.526638464 + 1.075

Combine like terms: 1.526638464 + 1.075 = 2.601638464
x = 2.601638464

Simplifying
x = 2.601638464

Subproblem 2
x + -1.075 = -1.526638464

Simplifying
x + -1.075 = -1.526638464

Reorder the terms:
-1.075 + x = -1.526638464

Solving
-1.075 + x = -1.526638464

Solving for variable 'x'.

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

Add '1.075' to each side of the equation.
-1.075 + 1.075 + x = -1.526638464 + 1.075

Combine like terms: -1.075 + 1.075 = 0.000
0.000 + x = -1.526638464 + 1.075
x = -1.526638464 + 1.075

Combine like terms: -1.526638464 + 1.075 = -0.451638464
x = -0.451638464

Simplifying
x = -0.451638464

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.601638464, -0.451638464}