To solve for $c$ in the equation $8 - 4c = -10 - 6c + 10$, follow these steps:

1. Simplify the right-hand side of the equation:

   $-10 - 6c + 10 = -6c$

   Now the equation is:

   $8 - 4c = -6c$

2. Add $6c$ to both sides of the equation:

   $8 - 4c + 6c = -6c + 6c$

   Simplifying this, we get:

   $8 + 2c = 0$

3. Subtract 8 from both sides of the equation:

   $8 + 2c - 8 = 0 - 8$

   Simplifying this, we get:

   $2c = -8$

4. Divide both sides by 2 to solve for $c$:

   $\frac{2c}{2} = \frac{-8}{2}$

   Simplifying this, we get:

   $c = -4$

So, the solution is $c = -4$.

Would you like more details or have any questions?

Here are 8 related questions to expand on this topic:

1. How would you solve the equation $5 - 3c = -15 - 7c + 15$?
2. What is the value of $c$ if the equation was $9 - 2c = -3 - 5c + 3$?
3. How do you check if your solution for $c$ is correct?
4. Can you graph the equations $8 - 4c$ and $-10 - 6c + 10$ to visually find the solution?
5. What are the steps to solve a system of linear equations involving $c$?
6. How would you solve for $c$ in the equation $7c + 5 = 3c - 9$?
7. Can you explain the difference between solving linear and quadratic equations?
8. How would you solve an equation involving absolute values, such as $8 - 4|c| = -10 - 6|c| + 10$?

Tip: Always combine like terms and simplify both sides of the equation before isolating the variable.