The mathematical content in the image appears to contain two expressions:

1. $z = x^2 + y^2 + 4x + 6y - 4$
2. A constraint (labeled "vincolo"): $4x + y - 6 = 0$

Let me know how you'd like to proceed. Here are some possibilities:

• Solve for $z$ under the constraint $4x + y - 6 = 0$.
• Analyze $z$ as a function of $x$ and $y$.
• Investigate the constraint or use it to eliminate one variable (e.g., solve for $y$ in terms of $x$ or vice versa).
• Find the extrema of $z$ given the constraint using methods like Lagrange multipliers.

Would you like me to solve or analyze this in detail?

Here are related follow-up questions:

1. How do you apply constraints to find extrema in multivariable functions?
2. What does the geometry of $z = x^2 + y^2 + 4x + 6y - 4$ represent?
3. How can we simplify $z$ using algebraic techniques?
4. How do Lagrange multipliers work when applied to $z$ with the constraint $4x + y - 6 = 0$?
5. What does the constraint $4x + y - 6 = 0$ represent geometrically?

Tip: When working with constraints, always consider substituting to reduce the number of variables for simpler calculations.