In an ideal market for any product the quantity supplied increases with the price of the product and the quantity demanded decreases with an increase in price. The opposite is true for a decrease in the price.
As the price of a product changes, the quantity supplied and the quantity demanded changes; when the two are equal a state of equilibrium is reached.
In the problem the quantity supplied is given by Qs = 100 + 3*P and the quantity demanded is given by Qd = 400 - (2*P + T) where T = 15. To determine the equilibrium price equate the two and solve for P. This gives: 100 + 3*P = 400 - (2*P + 15)
=> 100 + 3P = 400 - 2P - 15
=> 5P = 285
=> P = 57
The equilibrium price is equal to 57 and the equilibrium quantity is equal to 271.