The product of the first and third of three consecutive integers is 1 less than 5 times the second. find the integers

If x is the second integer, the problem statement tells you
  (x-1)(x+1) = 5x-1
  x² -1 = 5x -1
  x² -5x = 0
  x(x -5) = 0
The middle integer could be 0 or 5.

The three integers could be {-1, 0, 1} or {4, 5, 6}.