Problem Solving

Please help!
{-10; -6; -5; -4; -2.5; -1; 0; 2.5; 4; 6; 7; 10}
A number is to be selected at a random from the set above. What is the probability that the number selected will be a solution of the equation (x-5)(x+10)(2x-5)=0?
1/12
1/6
1/4
1/3
1/2
answer is 1/6

solutions are,x = 2.5, -10, 5. There are only two of those in the set. So 2/12 or 1/6

How did you solve the equation? I'm drawing blanks tonight

Simple approach :

To be a solution of the equation the value of X should make atleast 1 of the factors 0

If (x-5)(x+10)(2x-5)=0,

If x is 5,(x-5)=0 and thus is a solution
If x is -10.(x+10)=0 and this is a solution

Now from the given set only -10 and 2.5 will make the expression as 0.

Therefore : P(X will be a solution) = 2c1/12c1 = 1/6