-16t² + 32t + 128 = 0
-16t² + 64t - 32t + 128 = 0
-16t(t - 4) - 32(t - 4)
(-16t - 32)(t - 4) = 0
-16t -32 = 0 Â Â Â t - 4 = 0
-16t = 32 Â Â Â Â Â t = 4
t = -2
t = -2 and t = 4 are the values that makes S = 0.
Yes, because if you apply either of  these values alone, S will be 0.