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

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

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

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

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

Multiply (-2 + 3x) * (1 + 2x)
(-2(1 + 2x) + 3x * (1 + 2x)) = (2x + -1)(x + 3)
((1 * -2 + 2x * -2) + 3x * (1 + 2x)) = (2x + -1)(x + 3)
((-2 + -4x) + 3x * (1 + 2x)) = (2x + -1)(x + 3)
(-2 + -4x + (1 * 3x + 2x * 3x)) = (2x + -1)(x + 3)
(-2 + -4x + (3x + 6x2)) = (2x + -1)(x + 3)

Combine like terms: -4x + 3x = -1x
(-2 + -1x + 6x2) = (2x + -1)(x + 3)

Reorder the terms:
-2 + -1x + 6x2 = (-1 + 2x)(x + 3)

Reorder the terms:
-2 + -1x + 6x2 = (-1 + 2x)(3 + x)

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

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

Solving
-2 + -1x + 6x2 = -3 + 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
-2 + 3 + -1x + -5x + 6x2 + -2x2 = -3 + 5x + 2x2 + 3 + -5x + -2x2

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

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

Combine like terms: 6x2 + -2x2 = 4x2
1 + -6x + 4x2 = -3 + 5x + 2x2 + 3 + -5x + -2x2

Reorder the terms:
1 + -6x + 4x2 = -3 + 3 + 5x + -5x + 2x2 + -2x2

Combine like terms: -3 + 3 = 0
1 + -6x + 4x2 = 0 + 5x + -5x + 2x2 + -2x2
1 + -6x + 4x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
1 + -6x + 4x2 = 0 + 2x2 + -2x2
1 + -6x + 4x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1 + -6x + 4x2 = 0

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

Divide each side by '4'.
0.25 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1.5x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -1.5x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1.5x + x2 = 0 + -0.25
-1.5x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-1.5x + x2 = -0.25

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -0.25 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -0.25 + 0.5625

Combine like terms: -0.25 + 0.5625 = 0.3125
0.5625 + -1.5x + x2 = 0.3125

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(x + -0.75) equal to 0.559016994 and -0.559016994.

Subproblem 1
x + -0.75 = 0.559016994

Simplifying
x + -0.75 = 0.559016994

Reorder the terms:
-0.75 + x = 0.559016994

Solving
-0.75 + x = 0.559016994

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 0.559016994 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 0.559016994 + 0.75
x = 0.559016994 + 0.75

Combine like terms: 0.559016994 + 0.75 = 1.309016994
x = 1.309016994

Simplifying
x = 1.309016994

Subproblem 2
x + -0.75 = -0.559016994

Simplifying
x + -0.75 = -0.559016994

Reorder the terms:
-0.75 + x = -0.559016994

Solving
-0.75 + x = -0.559016994

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -0.559016994 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -0.559016994 + 0.75
x = -0.559016994 + 0.75

Combine like terms: -0.559016994 + 0.75 = 0.190983006
x = 0.190983006

Simplifying
x = 0.190983006

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.309016994, 0.190983006}