Let's factor the quadratic equation:

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

### Step 1: Simplify the equation
Factor out the greatest common factor (GCF), which is 2:

\[
2(x^2 - x - 6) = 0
\]

Now we focus on factoring \(x^2 - x - 6\).

### Step 2: Factor the quadratic
We need two numbers that multiply to \(-6\) (the constant term) and add to \(-1\) (the coefficient of \(x\)).

The numbers are \(-3\) and \(2\) because:

\[
-3 \times 2 = -6 \quad \text{and} \quad -3 + 2 = -1
\]

Now, factor the quadratic:

\[
x^2 - x - 6 = (x - 3)(x + 2)
\]

### Step 3: Final factored form
Thus, the factored form of the original equation is:

\[
2(x - 3)(x + 2) = 0
\]

### Step 4: Solve for \(x\)
Set each factor equal to zero:

1. \(x - 3 = 0 \quad \Rightarrow \quad x = 3\)
2. \(x + 2 = 0 \quad \Rightarrow \quad x = -2\)

### Solutions:
The solutions are:

\[
x = 3 \quad \text{or} \quad x = -2
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you factor quadratics when the leading coefficient isn't 1?
2. What is the method to solve quadratic equations using the quadratic formula?
3. Can you solve any quadratic equation by factoring?
4. How do you apply the GCF in factoring higher-degree polynomials?
5. What happens if the discriminant in a quadratic equation is negative?

### Tip:
Always check if there's a common factor (like 2 in this problem) to simplify the quadratic before factoring further!

Learn how to factor the quadratic equation 2x^2 - 2x - 12 using the GCF and factoring techniques. This problem introduces key algebraic concepts, such as the zero product property and factoring theorem, suitable for students in Grades 8-10.

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