Question: 2$x^2$ = -10$x$
1. **State the problem:** Solve the quadratic equation $$2x^2 = -10x$$.
2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:
$$2x^2 + 10x = 0$$
3. **Factor the equation:** Factor out the common factor $2x$:
$$2x(x + 5) = 0$$
4. **Apply the zero product property:** Set each factor equal to zero:
$$2x = 0 \implies x = 0$$
$$x + 5 = 0 \implies x = -5$$
5. **Final answer:** The solutions to the equation are $$x = 0$$ and $$x = -5$$.