https://file.aiquickdraw.com/mathbot/file/172735692846544rrttzq.jpg

The equation in the image is:

\[
-3x^2 - 12x = 0
\]

We are asked to solve this by factoring out the Greatest Common Factor (GCF).

### Step 1: Find the GCF

The terms in the equation are \(-3x^2\) and \(-12x\). The common factor between them is \(-3x\), since:

- Both terms have a common factor of \(-3\),
- Both terms include \(x\).

### Step 2: Factor out the GCF

Factoring out \(-3x\) from the equation:

\[
-3x(x + 4) = 0
\]

### Step 3: Solve for \(x\)

Now we solve the factored equation by setting each factor equal to zero.

1. From \(-3x = 0\), we get:
   \[
   x = 0
   \]

2. From \(x + 4 = 0\), we get:
   \[
   x = -4
   \]

### Final Answer:
The solutions are:
\[
x = 0 \quad \text{or} \quad x = -4
\]

Would you like any further explanation on the steps or concepts? 

Here are 5 related questions:
1. How do you factor quadratic equations when the GCF isn't obvious?
2. Can you solve quadratic equations using methods other than factoring?
3. What is the quadratic formula, and when is it used?
4. How can you check if the solutions to a factored equation are correct?
5. What are the properties of parabolas associated with quadratic equations?

**Tip:** Always check for a GCF before proceeding with factoring or applying other methods for solving equations.

Solve the following equations by factoring out the GCF: -3x^2 - 12x = 0

Learn how to solve the quadratic equation -3x^2 - 12x = 0 by factoring out the greatest common factor (GCF). This step-by-step solution is ideal for students learning about factoring in algebra and quadratic equations. Suitable for Grades 8-10.

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