While it will not always be the case, start by assuming we are only dealing with integers and the factors of
x^2+7x-18
have the form
(x+a)(x-b) we know a and -b have different signs since their product is negative (-18)
We also know that a is greater than b since the coefficient of x is greater than zero.
There are only a limited number of possible integer values for a and b with a>b and ab = 18
(a,b) = (18,1) which would give a-b = 17; not what we want
(a,b) = (9,2) which would give a-b = 7; this matches the x coefficient of the given equation
(a,b)= (6,3) which would give a-b=3; not what we want
There are no other integer possibilities.
The factoring is
(x+9)(x-2) = x^2 + 7x -18
Since
x^2 + 7x - 18 = 0
either
x+9 = 0 or x-2=0
So
either x=-9 or x=2
