To solve for the value of $z$, we can substitute the given values of $x = 3$ and $y = -2$ into the equation:

$z = x^2 - 3y$

Substituting:

$z = (3)^2 - 3(-2)$

Now, simplify:

$z = 9 + 6$

$z = 15$

So, the value of $z$ is 15.

Would you like more details or have any other questions?

Here are 5 related questions to expand on the topic:

1. How do you solve for variables when multiple variables are involved?
2. What is the difference between solving a linear and a quadratic equation?
3. How do you approach word problems involving similar equations?
4. What would happen if the value of $y$ was positive instead of negative?
5. How would you solve this equation if it involved more complex terms?

Tip: When substituting values into equations, make sure to carefully follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).