a) x^2 +x -30 = 0 is factored by looking for two factors of 30 that differ by 1. We know ...
30 = 1*30 = 2*15 = 3*10 = 5*6
The last two factors differ by 1, so we can factor the trinomial as
(x +6)(x -5) = 0
b) The solutions are found by finding values of x that make these factors zero. The only way the product will be zero is if one or more of the factors is zero.
x + 6 = 0
x = -6 . . . . . subtract 6
x - 5 = 0
x = 5 . . . . . add 5
The solutions are x = -6 or x = 5
These are the values of x that will satisfy the equation (make it true). What they mean depends on the meaning of the variable and the situation the equation is a model of.