Step-by-step Answer:
Step 1:
Extract factor(s) common to all terms.
In this case, the HCF is 3, so the expression is written
-12x^2+45x+12 = -3(4x^2-15x-4)
The negative sign was also exrracted to give a positive leading coefficient, which is easier to work with.
Step 2, group the coefficient in such a way that there is a common factor.
Leaving the factor -4 for the moment, and concentrate on the coefficients in parentheses, write the original expression as
4x^2 - 15x -4
= 4x^2 -16x
+ x -4
= 4x*(x-4) + 1*(x-4)
extract (x-4) as a common factor
= (x-4)(4x+1)
Step 3:
Combine all the factors to get
-3(x-4)(4x+1)
=3(4-x)(4x+1)
as the complete factoring of the given expression.