Chapter R - Algebra Reference - R.5 Inequalities - R.5 Exercises - Page R-21: 40

$x^3+7x^2+12x\leq0$ $x(x^2+7x+12)\leq0$ $x(x+4)(x+3)\leq0$ $-3\leq x\leq 0$ and $x\leq-4$

Step 1: Factorize inequality (common factor) Step 2: Factorize expression inside brackets (Trinomial) Step 3: The function will be smaller than $0$ for $-3\leq x\leq 0$ and $x\leq-4$