the 2 consecutive negative integers can be written as

x and x - 1

where x is negative integer

the product of the 2 consecutive negative integers is 156

x(x - 1) = 156

by solving we find and consider the negative roots (since x<0)

x = -12

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-12 -1 = -13

indeed

(-12)*(-13) = 156

the 2 consecutive negative integers are -12 and -13.