1. **State the problem:** We are given the equation $$-3x^2 - 9x = -84$$ and need to find an equivalent equation from the options provided. 2. **Rewrite the equation:** To find an equivalent equation, we want to move all terms to one side to set the equation equal to zero. 3. **Add 84 to both sides:** $$-3x^2 - 9x + 84 = -84 + 84$$ $$-3x^2 - 9x + 84 = 0$$ 4. **Multiply both sides by -1 to make the leading coefficient positive:** $$\cancel{-1}(-3x^2 - 9x + 84) = \cancel{-1}(0)$$ $$3x^2 + 9x - 84 = 0$$ 5. **Conclusion:** The equivalent equation is $$3x^2 + 9x - 84 = 0$$ which matches the first option. This process shows how to rearrange and simplify the equation to standard quadratic form with a positive leading coefficient.