Do you want Google as your browser, of your search engine?

Type about:preferences#search<enter> in the address bar. Follow the directions.

Sometimes an add-on will switch your home page, your search engine, etc., and no matter how many times you change your settings on the Options page, your preferences are ignored. In that case, you need to get rid of those bad add-ons.

You can start on the Add-ons page. Either:

• Ctrl+Shift+a
• "3-bar" menu button (or Tools menu) > Add-ons

In the left column, click Extensions. Then case a critical eye over the list on the right side. If in doubt, disable. Bear in mind that all extensions are optional, none come with Firefox.

Often a link will appear above at least one disabled extension to restart Firefox. You can complete your work on the tab and click one of the links as the last step.

Does that allow you to regain control of your settings?

Firefox itself is a web browser. The Bing and Google are search engine sites.