The expression you're looking to simplify is:

$3c^2 + 6c + 4 - c^2 + c$

Now, let's break it down:

1. Combine like terms:

   • $3c^2$ and $-c^2$ are both $c^2$ terms.
   • $6c$ and $c$ are both $c$ terms.
   • The constant term is $4$.

2. Simplifying: $3c^2 - c^2 = 2c^2$ $6c + c = 7c$ So the expression simplifies to: $2c^2 + 7c + 4$

Thus, the fully simplified form is: $2c^2 + 7c + 4$

Would you like more details or have any further questions?

Here are some related questions to explore:

1. What is the process for factoring quadratic expressions like $2c^2 + 7c + 4$?
2. How do you handle expressions with higher powers of $c$ (like $c^3$) in a similar manner?
3. Can you solve a quadratic equation such as $2c^2 + 7c + 4 = 0$?
4. How would you simplify expressions with more than one variable, such as $3x^2 + 6x + 4y^2$?
5. What are some common techniques for simplifying rational expressions involving polynomials?

Tip: Always group similar terms (like terms with the same degree) to simplify the expression step by step!