1. **State the problem:** Solve the quadratic equation $3x^2 - 6x = 0$ for $x$. 2. **Formula and rules:** To solve quadratic equations, we can factorize the expression and use the zero product property which states if $ab=0$, then either $a=0$ or $b=0$. 3. **Factor the equation:** $$3x^2 - 6x = 3x(x - 2) = 0$$ 4. **Apply zero product property:** Set each factor equal to zero: $$3x = 0 \quad \text{or} \quad x - 2 = 0$$ 5. **Solve each equation:** $$x = \cancel{\frac{0}{3}}0$$ $$x = 2$$ 6. **Final answer:** The solutions to the equation are $x = 0$ and $x = 2$.