State tax filing

I stopped by a local tax office in Georgia and confirmed that if my company has my place of employment listed here in Ga, then what you are talking about applies to me. Therefore, since Texas has no state income tax (which is a joke because Texas collects its state income tax through property taxes (on a $400K house one would pay 3% or $12,000 a year in property tax in Texas vs $1,500 in Ga.) and I would be paying about $10K a year in Georgia Tax plus the 3% per year on a house in Texas. I will take the new position in Texas so I do not get double taxed, Thanks for all the replies!