The equation is:

$x^2 + x - 2 = 0$

To solve it, we can factor the quadratic equation. We need two numbers that multiply to $-2$ and add up to $1$. These numbers are $2$ and $-1$, because:

$2 \times (-1) = -2 \quad \text{and} \quad 2 + (-1) = 1$

So, we can factor the equation as:

$(x + 2)(x - 1) = 0$

Now, apply the zero-product property:

$x + 2 = 0 \quad \text{or} \quad x - 1 = 0$

Solving each:

1. $x + 2 = 0 \quad \Rightarrow \quad x = -2$
2. $x - 1 = 0 \quad \Rightarrow \quad x = 1$

Thus, the solutions are:

$x = -2 \quad \text{or} \quad x = 1$

Would you like a more detailed explanation or help with another problem?

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Here are some related questions for you to explore:

1. How do you solve a quadratic equation using the quadratic formula?
2. What are the properties of quadratic equations that determine the number of solutions?
3. How do you factor more complex quadratic equations?
4. What happens when a quadratic equation cannot be factored easily?
5. What is the discriminant, and how does it affect the nature of the solutions?

Tip: Always check your solutions by substituting them back into the original equation to ensure they satisfy it!