Given the equation $a = b - c + d$, we need to solve for $c$. To isolate $c$, follow these steps:

1. Start with the given equation: $a = b - c + d$

2. Subtract $b$ and $d$ from both sides to isolate the term involving $c$: $a - b - d = -c$

3. Multiply both sides by $-1$ to solve for $c$: $c = b + d - a$

So, the formula to solve for $c$ is: $c = b + d - a$

Would you like further details or have any questions?

Here are five related questions to expand on this topic:

1. If $b = 5$, $d = 3$, and $a = 4$, what is the value of $c$?
2. How would the formula change if the original equation was $a = b + c - d$?
3. Can you derive $d$ in terms of $a$, $b$, and $c$ from the original equation?
4. What happens to the formula if all variables are positive integers?
5. How can this equation be applied in a real-world scenario?

Tip: When solving for a variable, aim to isolate that variable on one side of the equation by using inverse operations.