First simplify the expression:
2(2t2-7t+5). All we need now are the roots (zeroes) of 2t2-7t+5, which is now easier to factorise:
(2t-5)(t-1). The roots are when either 2t-5=0 or t-1=0, Solve these two equations for t:
2t-5=0, 2t=5, t=5/2; or t-1=0, t=1. These are the roots: t=5/2 or 1.