Step 1 :The question is asking to solve for $c$ in the equation $6c + 14 = -5c + 4 + 9c$.
Step 2 :First, we need to simplify the equation by combining like terms.
Step 3 :Then, we can isolate $c$ on one side of the equation by subtracting $14$ from both sides.
Step 4 :Finally, we can solve for $c$ by dividing both sides of the equation by the coefficient of $c$.
Step 5 :The solution to the equation is $c = \boxed{-5}$.