1. State the problem: Solve the quadratic equation $2x^2+4x=0$. 2. Factor the equation: Factor out the greatest common factor $2x$: $$2x(x+2)=0$$ 3. Apply the zero product property: Set each factor equal to zero: $$2x=0 \quad \Rightarrow \quad x=0$$ $$x+2=0 \quad \Rightarrow \quad x=-2$$ 4. Conclusion: The solutions to the equation $2x^2+4x=0$ are $x=0$ and $x=-2$.