The Fastecosearch.com website hosts a basic search engine that is not likely to offer you high-quality service. The Fastecosearch.com search aggregator uses the Bing.com service to deliver results for the users' search queries. This means that the Fastecosearch.com page is safe to use.
The Fastecosearch.com website is likely promoted via PUPs (Potentially Unwanted Programs). Such applications often pose as useful utilities while their only goal is to change the settings of the user's Web browser to set up an affiliated website as their default new tab page. This way, the PUP aids the affiliated page in generating both traffic and revenue. Despite the fact that the Fastecosearch.com site is not harmful, there is no guarantee that the PUP installed on your computer will not change your settings again and redirect you to an unreliable or potentially unsafe website.
There is a strong recommendation from malware experts to download and install a genuine anti-malware utility that will scan your system, locate, and remove any PUPs that may be meddling with your computer's configurations quickly and safely.