Answer
$3x^3-9x^2-12x\gt0$
$3x(x^2-3x-4)\gt0$
$3x(x+1)(x-4)\gt0$
$-1\lt x\lt0$ and $4\lt x$
Work Step by Step
Step 1: Factorize inequality (common factor $3x$)
Step 2: Factorize expression inside brackets (trinomial)
Step 3: The function will be greater than $0$ for $-1\lt x\lt0$ and $4\lt x$
