18x^2 +9x -20
= (3x+4)(6x-5)
if you have trouble factoring, as a very last resort
use the quadratic formula
x = -9/36 +/- (1/36)(sqr(81+4(18)(20))
= -1/4 +/-sqr1521/36 = -1/4 +/-39/36
= 30/36, -48/36
= 5/6, - 4/3
then take each solution, change its sign and stick an x in front of it
(x-5/6)(x+4/3)
=(1/6)(6x-5)(1/3)(3x+4)
= (1/18)(6x-5)(3x+4)
= (1/18)(18x^2 -15x+24x -20)
= (1/18)(18x^2 +9x -20)
which is the original polynomial compressed by a factor of 18
or another approach is take factors of -20, the constant term and divide by factors of 18, the coefficient of the highest degree term
-4,-5,4,5 and 9,2,3,3
try them out, one at a time, such as
-4/3 gives (x+4/3), multiply by 3 to get 3x+4 is one factor
divide 3x+4 into 18x^2+9x-20 to get 6x-5 the other factor
that's also time consuming, but it works and narrows down the possibilities
18x^2+ 9x -20 factors to (ax+b)(cx+d) where ac=18, bd=-20
ad+bc = 9, that's 3 equations 4 unknowns, but there's one more restriction, a,b,c and d are all integers
which leads to a unique solution
ac=6(3), bd=(-5)(4)
(6x-5)(3x+4)
= 18x^2 -15x+24x -20
= 18x^2 +9x-20
but basic method of factoring is just trial and error, keep trying different combinations
of (ax+b)(cx+d) where a and c are factors of 18, and b and d are factors of -20
