To solve the equation \(7c + 12 = -4c + 78\), we need to isolate the variable \(c\). Here are the steps:

### Step-by-step Solution:

1. **Combine like terms**: Add \(4c\) to both sides to bring all the \(c\) terms to one side.
   
   \[
   7c + 4c + 12 = -4c + 4c + 78
   \]
   
   This simplifies to:
   
   \[
   11c + 12 = 78
   \]

2. **Isolate the term with \(c\)**: Subtract 12 from both sides.

   \[
   11c + 12 - 12 = 78 - 12
   \]
   
   This simplifies to:
   
   \[
   11c = 66
   \]

3. **Solve for \(c\)**: Divide both sides by 11.

   \[
   \frac{11c}{11} = \frac{66}{11}
   \]

   This simplifies to:

   \[
   c = 6
   \]

### Conclusion:

The solution to the equation \(7c + 12 = -4c + 78\) is \(c = 6\).

Would you like more details on any of the steps or have any other questions?

### Related Questions:

1. How would you solve the equation if it were \(7c + 12 = -4c + 100\)?
2. What happens if the variable is on both sides with different coefficients?
3. How can we check if our solution \(c = 6\) is correct?
4. Can we use the same steps to solve inequalities involving variables?
5. How does adding or subtracting a constant affect an equation?

**Tip**: Always verify your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation 7c + 12 = -4c + 78 step-by-step. This problem involves solving linear equations by combining like terms and isolating the variable. Suitable for students in Grades 7-9 studying algebra.

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