The equation you provided is:

\[
3x^2 + 2y^2 - z = -4
\]

This equation has three variables: \( x \), \( y \), and \( z \). Let's try to isolate \( z \) to better understand it:

### Step 1: Isolate \( z \)
\[
3x^2 + 2y^2 - z = -4
\]

Add \( z \) to both sides:
\[
3x^2 + 2y^2 = z - 4
\]

Now, add 4 to both sides to isolate \( z \):
\[
z = 3x^2 + 2y^2 + 4
\]

This shows that \( z \) is a function of \( x \) and \( y \).

Would you like a further detailed explanation or additional questions related to this equation?

### Relative Questions:
1. What would the graph of this equation look like in 3D space?
2. How does changing the coefficients of \( x^2 \) and \( y^2 \) affect the function?
3. How can we express this equation in polar coordinates?
4. What is the value of \( z \) if \( x = 1 \) and \( y = 2 \)?
5. How does this equation compare to the equation of an ellipse?

### Tip:
When dealing with equations involving multiple variables, isolating one variable can often make the relationships between the variables easier to understand.

Understand how to solve the multivariable equation 3x^2 + 2y^2 - z = -4. This solution includes isolating the variable z and analyzing the quadratic relationships in x and y. Suitable for students in Grades 10-12 learning algebra and quadratic functions.

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