I do not understand the answer in 1.a)

Why isn't the profit function 75q - (q² + 25q + 144) ?

I got q = 50 but the answer is q = 25.

Why is it that we put - in front of every number instead of + when we put the cost function in the profit function.

1. Lelu runs a firm that sells multipasses to intergalactic cruises. Her short-run cost function is given by C(q) = q2 + 25q + 144 (a) If the market price is $75/pass, how many units will Lelu produce? (b) At what price will Lelu earn zero profits? (c) If the price is below the level you found in b., will Lelu shut down? If so, explain. If not, below what price will she shut down? Answer: (a) Profit = 75q - C(q) = 75q - q2 - 25q 144 Max profit --> dProfit/dq = 0 75 - 2q -25 =0 q = 25