This reminds me of the combinatorial theory, specifically a problem of variation. The question:

The product of three consecutive numbers is 3360. What are the numbers?

We can consider it as the number of variations of m elements taken n to n, is equal to the product of n consecutive and decreasing factors starting from , so that:

.

with the following data n= 3 y V_m,3= 3360. So:

It is clear that the cubic equations have 3 possible solutions, one of them is a real number, which is of our interest, therefore by the method of Cardano we can obtain this number:

with R= 1678, Q=-3/9 and a₁=-3 we have:

In order for the variation to be fulfilled we have:

It is resolved. by @juancmz