I read this as (12x^3-48x^2-75x-24)/(6x+3). Divide top and bottom by 6: 2x^3-8x^2-12.5x-4)/(x+1/2).
We can use synthetic division:
-1/2 | 2 -8 -12.5 -4
.........2 -1....4.5..4
.........2 -9......-8 | 0 = 2x^2-9x-8
Provided x≠-1/2 the quotient is 2x^2-9x-8 which is a simplification of the original expression.