If 2x + 7 is a factor, then x = -7/2 is a zero....so.....
6(-7/2)^3 + 19(-7/2)^2 + c(-7/2) + 35 = 0
-6 (343/ 8) + 19 (49/4) - (7/2)c + 35 = 0
-2058 / 8 + 931/4 - (7/2)c + 35 = 0
[ -2058 + 1862 + 280 ] / 8 - (7/2)c = 0
21/2 - (7/2)c = 0
21 - 7c = 0
21 = 7c
c = 3
