To solve the equation (2x+1)(3y-2) = -55, we can start by expanding the expression on the left side:

(2x+1)(3y-2) = -55
6xy - 4x + 3y - 2 = -55

Next, we can rearrange the equation to isolate the terms involving x and y:

6xy - 4x + 3y = -55 + 2
6xy - 4x + 3y = -53

Now, we can try to factor out common terms from the left side of the equation:

2(3xy - 2x) + 3y = -53

At this point, it doesn't seem possible to factor out any common terms further. Therefore, we can proceed to solve for x and y by setting the equation equal to zero:

2(3xy - 2x) + 3y + 53 = 0

This equation does not have a simple solution for x and y.