Answer:
x= 2, y= 2, and z= 6
Step-by-step explanation:
If this is a Diophantine equation, add 35 to both sides and factor the left:
(3x+1)(2y+7)(z+5) = 847 = 7 times 112
Each integer factorization of 847 into 3 factors leads to a different number/value of x, y, and z. If the first factor, (3x+1), is 1 more than a multiple of 3, and the second factor, (2y+7), is odd, then x, y, and z will be integers.
For example:
847 = 121 times -7 times -1 gives (x, y, z) = (40, -7, -6) because 121 times -7 times -1 is 847 as well, it checks out.
If x, y, and z need to be positive, then the three numbers/factors need to be greater than 1, 7, and 5. The only combination that works is 7 times 11 times 11, which gives (x, y, z) = (2, 2, 6).
:)
