What are the roots of the equation x^2+3x-18=0

First you open 2 parenthesis with x in each one:

(x )(x )=0

Then, you place the sign of the second term (the x term) in the first parenthesis.

(x+ )(x )=0

Next, you multiply the signs of the x term and the sign of the constant (the third term).
Since + × - = -, then you place a -.

(x+ )(x- )=0

You look at the constant (-18) and the second term (3). What two numbers multiplied give you -18 but subtracted (since the signs inside the parenthesis are opposite) give you 3? Those numbers are 6 and 3.
Since the result of the substraction need to be 3, you place the 6 with the + sign and the 3 with the negative sign (if you think of it, 6-3=3 but 3-6 = -3. That's the reason behind placing the numbers)

(x+6)(x-3)=0

Therefore,

x+6=0 or x-3=0

x=-6 or x=3

Your roots are -6 and 3.