1. **State the problem:** Solve for $x$ when $f(x) = 0$ given the function $f(x) = -\frac{1}{30}(x+3)(x-27)$. 2. **Formula and rules:** To find the roots of a function, set the function equal to zero and solve for $x$. Since this is a product of factors, the zero product property applies: if $ab=0$, then either $a=0$ or $b=0$. 3. **Set the function equal to zero:** $$-\frac{1}{30}(x+3)(x-27) = 0$$ 4. **Divide both sides by $-\frac{1}{30}$ to isolate the product:** $$\cancel{-\frac{1}{30}}(x+3)(x-27) = \cancel{-\frac{1}{30}} \times 0$$ $$ (x+3)(x-27) = 0 $$ 5. **Apply zero product property:** $$x+3=0 \quad \text{or} \quad x-27=0$$ 6. **Solve each equation:** $$x = -3 \quad \text{or} \quad x = 27$$ 7. **Final answer:** The solutions to $f(x)=0$ are $x = -3$ and $x = 27$.