To simplify this expression, we first need to find a common denominator for the fractions on both sides of the equation.

The common denominator for 4 and 5 is 20. So, we rewrite the expression as:

(20)(3x - 4) = (20)(2x + 1)

Expanding both sides, we get:

60x - 80 = 40x + 20

Next, we can combine like terms:

60x - 40x = 20
-80 - 20 = -100

So the simplified equation is:

20x = -100

Solving for x, we divide both sides by 20:
x = -5

Therefore, the solution to the equation is x = -5.