You're correct; it is more accurate to say "dividing both sides by -1" to simplify the equation. Let's restate the steps properly:

Given the equation after moving all terms to one side: $-x^2 - 5x - 4 = 0$

To factorize: $- (x^2 + 5x + 4) = 0$ $- (x + 4)(x + 1) = 0$

Next, to remove the negative sign: $(x + 4)(x + 1) = 0$

So, solving for $x$: $x = -4 \quad \text{or} \quad x = -1$

Here, dividing both sides by -1 effectively removes the negative sign on the left side of the equation.

Would you like more details or have any other questions?

Here are some related questions to further explore the topic:

1. What are the implications of having a negative sign in front of a quadratic equation?
2. How do you factorize polynomials of higher degrees?
3. What are the different methods to solve polynomial equations?
4. How do you determine the number of real roots of a polynomial equation?
5. What is the significance of the roots of an equation in graphing the polynomial?
6. How do you handle complex roots in quadratic equations?
7. What are the applications of quadratic equations in real-life problems?
8. How does the discriminant help in determining the nature of the roots?

Tip: When solving any equation, always verify each step carefully to ensure the operations you perform (like dividing or multiplying) are applied correctly, as this helps avoid errors in your final solution.