What's the difference between factoring an expression and solving an equation?

you can factor in order to solve. To solve means to find out what the unknown variable is. You "solve" for x, so that you have a solution in the form of x=a number. solving requires an equation.

to factor means to write as a product as in 6=2x3, the six is written as a product of 2 and 3. The 2 and 3 are factors of 6.

example problem where you do both.

x^2 + 7x + 10 = 0

I want to SOLVE FOR X, and I can do that by factoring the expression first. So, I'm writing it as a product of two factors:

(x + 2)(x + 5) = 0

now it's factored, but I still need to solve for x, and can do that by applying the "zero product property":

(x + 2) = 0 or (x + 5) = 0

now I solve each small equation and get the solution:

x = -2 or x = -5

that's it! ;)