let

x and x+1 be the two consecutive integers, where x is integer

the product of x and x+1 is 12

x(x + 1) = 12

x^2 + x - 12 = 0

solving the quadratic equation we find

x1 = 3

x2 = -4

thus we have 2 solutions:

first solution: 3 and 4

second solution: -4 and -3