1. **State the problem:** Solve the quadratic equation $2x^2 - 8x = 0$ 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:** $$2x^2 - 8x = 0$$ Factor out the common factor $2x$: $$2x(x - 4) = 0$$ 4. **Apply zero product property:** Set each factor equal to zero: $$2x = 0 \quad \text{or} \quad x - 4 = 0$$ 5. **Solve each equation:** $$x = 0$$ $$x = 4$$ 6. **Final answer:** The solutions to the equation $2x^2 - 8x = 0$ are $x = 0$ and $x = 4$.