First, let's expand the left side of the equation:

(2x + 3)(x + 1) + 8
= 2x^2 + 2x + 3x + 3 + 8
= 2x^2 + 5x + 11

Now, let's expand the right side of the equation:

(2x + 1)(x + 5)
= 2x^2 + 10x + x + 5
= 2x^2 + 11x + 5

Now, equate the two sides of the equation:

2x^2 + 5x + 11 = 2x^2 + 11x + 5

Subtracting 2x^2 from both sides, we get:

5x + 11 = 11x + 5

Subtracting 5x from both sides, we get:

11 = 6x + 5

Subtracting 5 from both sides, we get:

6 = 6x

Dividing by 6 on both sides, we get:

x = 1

Therefore, the solution to the equation is x = 1.