4(c-3)+3(c+3)=7c-3

To solve the equation \( 4(c-3) + 3(c+3) = 7c - 3 \), we will first expand both sides and then combine like terms.

1. Expand the left side: \[ 4(c - 3) = 4c - 12 \] \[ 3(c + 3) = 3c + 9 \] So, the left side becomes: \[ 4c - 12 + 3c + 9 = 7c - 3 \]

2. Combine like terms: \[ (4c + 3c) + (-12 + 9) = 7c - 3 \] This simplifies to: \[ 7c - 3 = 7c - 3 \]

3. Compare both sides:

   Since both sides of the equation are equal, \( 7c - 3 = 7c - 3 \), this indicates that the equation is true for all values of \( c \).

Thus, the solution is that the equation holds for all \( c \) (it's an identity).