I have the inverted market demand of $P=4Z-(q_1+q_2)$ and cost function of both firms is equal to $C=cq_i+f$ for $i=1,2$
So now, the existing firm wants to discourage a possible challenger to entry and sets an output that would make the profits of the challenger equal to 0.
My approach would be, to set up the profit function for the challenger:
Step 1: $(4Z-q_1-q_2)*q_2 - cq_2 = 0$ and then solve for $q_1$ in terms of $q_2$.
Step2: Then I can substitute $q_1$ in the profit function of firm 1 and take the derivative of the profit function with regard to $q_2$
Step3: The result of step 2 I would insert in step 1 in order to receive the quantity that firm one needs to produce in order to set the profit function of the challenger equal to zero.
Is this approach correct? I am a bit confused because of the strange algebra, but I could not come up with a different solution.