(5x-1)(2x+3)=2x

Solution for (5x-1)(2x+3)=2x equation:

Simplifying
(5x + -1)(2x + 3) = 2x

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

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

Multiply (-1 + 5x) * (3 + 2x)
(-1(3 + 2x) + 5x * (3 + 2x)) = 2x
((3 * -1 + 2x * -1) + 5x * (3 + 2x)) = 2x
((-3 + -2x) + 5x * (3 + 2x)) = 2x
(-3 + -2x + (3 * 5x + 2x * 5x)) = 2x
(-3 + -2x + (15x + 10x2)) = 2x

Combine like terms: -2x + 15x = 13x
(-3 + 13x + 10x2) = 2x

Solving
-3 + 13x + 10x2 = 2x

Solving for variable 'x'.

Reorder the terms:
-3 + 13x + -2x + 10x2 = 2x + -2x

Combine like terms: 13x + -2x = 11x
-3 + 11x + 10x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-3 + 11x + 10x2 = 0

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

Divide each side by '10'.
-0.3 + 1.1x + x2 = 0.0

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + 1.1x + 0.3 + x2 = 0.0 + 0.3

Reorder the terms:
-0.3 + 0.3 + 1.1x + x2 = 0.0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + 1.1x + x2 = 0.0 + 0.3
1.1x + x2 = 0.0 + 0.3

Combine like terms: 0.0 + 0.3 = 0.3
1.1x + x2 = 0.3

The x term is 1.1x.  Take half its coefficient (0.55).
Square it (0.3025) and add it to both sides.

Add '0.3025' to each side of the equation.
1.1x + 0.3025 + x2 = 0.3 + 0.3025

Reorder the terms:
0.3025 + 1.1x + x2 = 0.3 + 0.3025

Combine like terms: 0.3 + 0.3025 = 0.6025
0.3025 + 1.1x + x2 = 0.6025

Factor a perfect square on the left side:
(x + 0.55)(x + 0.55) = 0.6025

Calculate the square root of the right side: 0.776208735

Break this problem into two subproblems by setting 
(x + 0.55) equal to 0.776208735 and -0.776208735.

Subproblem 1
x + 0.55 = 0.776208735

Simplifying
x + 0.55 = 0.776208735

Reorder the terms:
0.55 + x = 0.776208735

Solving
0.55 + x = 0.776208735

Solving for variable 'x'.

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

Add '-0.55' to each side of the equation.
0.55 + -0.55 + x = 0.776208735 + -0.55

Combine like terms: 0.55 + -0.55 = 0.00
0.00 + x = 0.776208735 + -0.55
x = 0.776208735 + -0.55

Combine like terms: 0.776208735 + -0.55 = 0.226208735
x = 0.226208735

Simplifying
x = 0.226208735

Subproblem 2
x + 0.55 = -0.776208735

Simplifying
x + 0.55 = -0.776208735

Reorder the terms:
0.55 + x = -0.776208735

Solving
0.55 + x = -0.776208735

Solving for variable 'x'.

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

Add '-0.55' to each side of the equation.
0.55 + -0.55 + x = -0.776208735 + -0.55

Combine like terms: 0.55 + -0.55 = 0.00
0.00 + x = -0.776208735 + -0.55
x = -0.776208735 + -0.55

Combine like terms: -0.776208735 + -0.55 = -1.326208735
x = -1.326208735

Simplifying
x = -1.326208735

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.226208735, -1.326208735}