1. **State the problem:** Solve the equation $-36a^2 = 8a$ for $a$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero: $$-36a^2 - 8a = 0$$ 3. **Factor the equation:** Factor out the common factor $-4a$: $$-4a(9a + 2) = 0$$ 4. **Apply the zero product property:** For the product to be zero, either factor must be zero: - $-4a = 0$ which simplifies to $a = 0$ - $9a + 2 = 0$ which simplifies to $9a = -2$ 5. **Solve for $a$ in the second equation:** $$a = \frac{-2}{9}$$ 6. **Final solutions:** $$a = 0 \quad \text{or} \quad a = -\frac{2}{9}$$ These are the values of $a$ that satisfy the original equation.