Question 368683
The trick to factoring these kinds of trinomials is to take the 1st constant(10) multiplied by the last constant (-2).  This is -20.  What two numbers multiplied together equal -20 but add together to equal the middle constant of your equation(-1).  Well that would be -5 and 4.  because -5*4=-20 and -5+4=-1

So to factor it we replace the -t with (-5t+4t) to get

10t^2-5t+4t-2=0  Then we need to factor by grouping
(10t^2-5t)+(4t-2)=0  
5t(2t-1)+2(2t-1)=0  Then we combine to make the two factors
(5t+2)(2t-1)=0  Set each factor equal to 0 and solve for t. 
5t+2=0   2t-1=0
t=-2/5   t=1/2 

Hope this helps!