Anyone can do good, believers and unbelievers are capable of doing the same. The world would be a better place if more and more people have the heart to do good, rather than evil. Which is often borne out of selfishness, than selfless altruism.
But if you think this is a way to ensure yourself to eternal life; you are greatly mistaken; for it's all together different if you attempt to meet God's standard of righteousness.
The Bible says that heart is deceitfully wicked above all things; who can know it (Jeremiah 17:9)? Jesus said that unless your righteousness surpass that of the Scribes and the Pharisees, you will in no wise, enter into the Kingdom. and in Romans 8:6-7, the carnal mind is enmity with God, for it is not subject unto God's laws, neither it can be.
Thus, in order to meet God's standard, you must understand that YOU CAN'T. No one can, and the worst thing is, that all of us have fallen short of God's glory by our own sins (Romans 3:23). Our sins separated us from a holy and righteous God (Isaiah 59:1-2), and because of the heinous nature of our sins, He must punish sin for what it is (Exodus 34:6-7).
But because God loved us also, He sent His Son down; He is fully God and fully Man, but without sin (John 1:1-3, 14, & Hebrews 4:15). He lived by the commandments, perfectly; but by that Law, He died in our place as if He is guilty of all (Deuteronomy 21:22-23 & 27:26). On the third day, He rose again, defeating death, and will return soon.
Salvation begins by repenting of your sins, and trusting Jesus Christ alone for your salvation (John 5:24); and once you believe, if you truly believe, you become a new creature (2 Corinthians 5:17). This means, you have a new nature who wants to glorify God (Isaiah 43:7). By obeying Him, through His word (2 Timothy 3:16-17).
The good deeds you do now, is for God's glory, and not mere personal satisfaction.