Signed auto contract without down payment… Then backed out! Help?!

I signed the auto contract after being pursuaded by the finance director at Honda dealership that if I didn't like the car, they will cancel the contract for me. I told the finance manager in the office that since I will be buying a used Honda Civic, I want to make sure my mechanic gives an approval upon the inspection before committing to buying the Civic. He then called the finance director to the room and they told me to bring the car back after taking to the mechanic if I didn't like the car. My concern is since I have already signed the contract, then return to inform them I didn't want to buy the car, will I be binding to the contract or they just are going to cancel it? I don't have any paperwork from them. No down payment has been made.

They were pissed after I changed my mind about not buying the Civic and opted out for the Toyota Camry near my house instead.

The main reason the deal didn't go through is because upon reading the contract, I realized the finance manager quoted me wrong and higher price than the internet price that I have agreed. Also he gaves me an interest rate that was way too high while I am qualified for lower APR (I done my research after left their Honda dealership).

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