Rental property in multiple states

I believe this is correct, just want to make sure.

LLC owns 3 properties in 3 states.  2 states had positive income, 1 state had negative income, bringing the total income for the LLC negative.

State of GA wants $5000 tax on the rental income in their state.

State of NC wants $8000 tax on the rental income in their state.

State of MI is negative.

My overall income on 1040 is also negative, so I get no state tax credit from the state I live in for the amounts paid to other states.

So I basically have to pay $13,000 state income tax when I made zero income for the year.

I believe this is correct, right?   It's just so wrong.