There are two solutions for the equation $x^2 - x - 6 = 0$. What is the product of these two solutions?
I notice that the equation is a quadratic equation, which means it has the form $ax^2 + bx + c = 0$. I also notice that the coefficient of $x^2$ is 1, which means I can try to factor the equation by finding two numbers that add up to the coefficient of $x$ and multiply to the constant term. In this case, the coefficient of $x$ is -1 and the constant term is -6. I think of two numbers that add up to -1 and multiply to -6. I realize that -3 and 2 are such numbers, since $(-3) + 2 = -1$ and $(-3) \times 2 = -6$. So I can factor the equation as $(x - 3)(x + 2) = 0$. Now, I use the zero product property, which says that if a product of factors is zero, then one of the factors must be zero. So I set each factor equal to zero and solve for $x$. I get $x - 3 = 0$ or $x + 2 = 0$. Solving for $x$, I get $x = 3$ or $x = -2$. These are the two solutions for the equation. To find the product of these two solutions, I multiply them together. I get $3 \times (-2) = -6$. 