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

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

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

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

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

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

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

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

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

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

Combine like terms: 6x + 1x = 7x
-2 + 1x + 6x2 = (3 + 7x + 2x2)

Solving
-2 + 1x + 6x2 = 3 + 7x + 2x2

Solving for variable 'x'.

Reorder the terms:
-2 + -3 + 1x + -7x + 6x2 + -2x2 = 3 + 7x + 2x2 + -3 + -7x + -2x2

Combine like terms: -2 + -3 = -5
-5 + 1x + -7x + 6x2 + -2x2 = 3 + 7x + 2x2 + -3 + -7x + -2x2

Combine like terms: 1x + -7x = -6x
-5 + -6x + 6x2 + -2x2 = 3 + 7x + 2x2 + -3 + -7x + -2x2

Combine like terms: 6x2 + -2x2 = 4x2
-5 + -6x + 4x2 = 3 + 7x + 2x2 + -3 + -7x + -2x2

Reorder the terms:
-5 + -6x + 4x2 = 3 + -3 + 7x + -7x + 2x2 + -2x2

Combine like terms: 3 + -3 = 0
-5 + -6x + 4x2 = 0 + 7x + -7x + 2x2 + -2x2
-5 + -6x + 4x2 = 7x + -7x + 2x2 + -2x2

Combine like terms: 7x + -7x = 0
-5 + -6x + 4x2 = 0 + 2x2 + -2x2
-5 + -6x + 4x2 = 2x2 + -2x2

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

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

Divide each side by '4'.
-1.25 + -1.5x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -1.5x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -1.5x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -1.5x + x2 = 0 + 1.25
-1.5x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-1.5x + x2 = 1.25

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 = 1.25 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 1.25 + 0.5625

Combine like terms: 1.25 + 0.5625 = 1.8125
0.5625 + -1.5x + x2 = 1.8125

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 1.8125

Calculate the square root of the right side: 1.346291202

Break this problem into two subproblems by setting 
(x + -0.75) equal to 1.346291202 and -1.346291202.

Subproblem 1
x + -0.75 = 1.346291202

Simplifying
x + -0.75 = 1.346291202

Reorder the terms:
-0.75 + x = 1.346291202

Solving
-0.75 + x = 1.346291202

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 = 1.346291202 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 1.346291202 + 0.75
x = 1.346291202 + 0.75

Combine like terms: 1.346291202 + 0.75 = 2.096291202
x = 2.096291202

Simplifying
x = 2.096291202

Subproblem 2
x + -0.75 = -1.346291202

Simplifying
x + -0.75 = -1.346291202

Reorder the terms:
-0.75 + x = -1.346291202

Solving
-0.75 + x = -1.346291202

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 = -1.346291202 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -1.346291202 + 0.75
x = -1.346291202 + 0.75

Combine like terms: -1.346291202 + 0.75 = -0.596291202
x = -0.596291202

Simplifying
x = -0.596291202

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.096291202, -0.596291202}