First 5 terms:
a,
a+d,
a+2d,
a+3d,
a+4d
———
5a+10d is the sum=0
a+4d=6, so a=6-4d. Substitute this in the other equation: 5(6-4d)+10d=0,
30-20d+10d=30-10d=0, so 10d=30, d=30/10=3; a=6-4×3=6-12=-6.
CHECK
-6, -3, 0, 3, 6 sum to zero when the first term is -6 and the common difference is 3.