The given mathematical expression is:

$15 + (-14) + (-7)$

To simplify this:

1. Start with $15 + (-14)$. This is equivalent to $15 - 14$, which equals 1.
2. Now, add $(-7)$ to the result: $1 + (-7) = 1 - 7 = -6$.

So, the simplified expression is:

$15 + (-14) + (-7) = -6$

Would you like any more details or have any questions about this?

Here are 5 related questions you might consider:

1. What happens when you add two negative numbers?
2. How do you subtract a negative number?
3. Can you explain the rules for adding and subtracting integers?
4. What is the effect of zero on addition or subtraction in such problems?
5. How would this process change if the signs were different?

Tip: When simplifying expressions with both positive and negative numbers, treat negatives like "subtraction" and positives like "addition" for clarity.