What kind of careers that have to involve politics and business?

You could major in political science and / or business as a student, then public policies for graduate school. You can work as a pressure group influencing people in Congress on behalf of companies. or you could work in a group discussion, research and policy determination.

• You could work in labor relations.
• Government offices such as mayor, governor, senator, etc always involve in politics and business.
• You could be a corporate lawyer who interacts with politicians.
• Or a judge.

Then

There's the whole issue of political campaigns, fundraising, event planning, speech writing.