#-12x^2 +x+20# is not a comfortable quadratic to work with because of the negative sign at the front.
There are 2 ways around the problem.
#1.# The last term is positive, so we can just re-arrange the terms to have a positive term at the beginning:
#20+x -12x^2# which will factorise as #(4-3x)(5+4x)#
#2.# Sometimes re-arranging will not work because the last term might be negative as well.
Divide #-1# out as a common factor. This has the effect of changing the signs.
#-12x^2 +x+20 = -1(12x^2 -x-20)#
This factorises as
#-(3x-4)(4x+5)#
The expression can be left like this, or the negative sign can be multiplied by EITHER of the two brackets. NOT BOTH!
#-(3x-4)(4x+5)#
OR
#(-3x+4)(4x+5) = (4-3x)(5+4x)#
OR
#(3x-4)(-4x-5)#
