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

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

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

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

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

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

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

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

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

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

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

Solving
-2 + 3x + 2x2 = 3 + 4x + x2

Solving for variable 'x'.

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

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

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

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

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

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

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

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

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -1x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -1x + x2 = 0 + 5

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

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

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 5 + 0.25

Combine like terms: 5 + 0.25 = 5.25
0.25 + -1x + x2 = 5.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + -0.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
x + -0.5 = 2.291287847

Simplifying
x + -0.5 = 2.291287847

Reorder the terms:
-0.5 + x = 2.291287847

Solving
-0.5 + x = 2.291287847

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 2.291287847 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 2.291287847 + 0.5
x = 2.291287847 + 0.5

Combine like terms: 2.291287847 + 0.5 = 2.791287847
x = 2.791287847

Simplifying
x = 2.791287847

Subproblem 2
x + -0.5 = -2.291287847

Simplifying
x + -0.5 = -2.291287847

Reorder the terms:
-0.5 + x = -2.291287847

Solving
-0.5 + x = -2.291287847

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -2.291287847 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -2.291287847 + 0.5
x = -2.291287847 + 0.5

Combine like terms: -2.291287847 + 0.5 = -1.791287847
x = -1.791287847

Simplifying
x = -1.791287847

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.791287847, -1.791287847}