Answer
$\{-\frac{7}{2}, -\frac{1}{3}, 0\}$
Work Step by Step
Step 1. Given $|6x^3+23x^2+7x|=0$, remove the absolute sign to get $6x^3+23x^2+7x=0$
Step 2. Factor and solve: $x(2x+7)(3x+1)=0$ which gives $x=-\frac{7}{2}, -\frac{1}{3}, 0$ or $\{-\frac{7}{2}, -\frac{1}{3}, 0\}$
