The equation you provided is:

$x^2 - 4x - 12 = 0$

To solve this quadratic equation, one of the most common methods is factoring, but I will first check if it factors easily.

The equation can be written as:

$x^2 - 4x - 12 = 0$

We are looking for two numbers that multiply to give -12 and add up to -4. These numbers are -6 and 2 because:

$-6 \times 2 = -12 \quad \text{and} \quad -6 + 2 = -4$

So, we can factor the equation as:

$(x - 6)(x + 2) = 0$

Now, set each factor equal to zero:

$x - 6 = 0 \quad \text{or} \quad x + 2 = 0$

Solving these gives:

$x = 6 \quad \text{or} \quad x = -2$

Thus, the solutions to the equation are:

$x = 6 \quad \text{and} \quad x = -2$

Let me know if you need further explanation or have any questions!

Here are five related questions you might find interesting:

1. How can we check if these solutions are correct by substituting them back into the original equation?
2. What other methods can be used to solve quadratic equations besides factoring?
3. How can the quadratic formula be used to solve the same equation?
4. What does the discriminant tell us about the nature of the solutions to a quadratic equation?
5. What happens if the quadratic equation cannot be factored?

Tip: When factoring quadratic equations, always look for two numbers that multiply to give the constant term and add to give the coefficient of the linear term.