Calculus with Applications (10th Edition)

$3x^3-9x^2-12x\gt0$ $3x(x^2-3x-4)\gt0$ $3x(x+1)(x-4)\gt0$ $-1\lt x\lt0$ and $4\lt x$
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 $4\lt x$