Find three consecutjve integers such that the sum of the first, twice the second, and three times the third is -76

"Let x - the first integer
x + 1 - the 2nd integer
x + 2 - the third integer

x + 2(x + 1) + 3(x + 2) = -76
x + 2x + 2 + 3x + 6 = -76
6x + 8 = - 76
6x = -76 - 8
6x = - 84
x = - 14 first integer
-14 + 1 = -13 2nd integer
-14 + 2 = -12 3rd integer
To check
-14 + 2(-13) + 3(-12) = -76
-14 - 26 - 36 = - 76
-76 = - 76

-14, -13, and -12 are the integers"