7t^2-13t-110=(7t+22)(t-5)=0, so t=5 or -22/7.
How did I factorise? The only factors of 7 are 1 and 7, so we need t and 7t as the first terms in the brackets. The factors of 110 are: (1,110), (2,55), (5,22), (10,11) so we know the numbers accompanying the t terms in the brackets must be in one of these pairs of factors. We also know that 7 times one factor minus 1 times the other factor must be equal to 13, so we try out the possibilities until the difference comes out as 13. 7*5-1*22=35-22=13. Finally, we know there must be a plus in one bracket and a minus in the other. To get -35+22=-13 we need -5 in one bracket and +22 in the other.