Verse 7 says, "Casting all your care upon Him, for He careth for you." Jesus said that we could cast all our cares upon Him, not just some. While here on earth we will have cares and tribulations. But Jesus said in John 16:33 that we are to be of good cheer, because He has overcome the world.
Jesus didn't promise that life with Him would be care free, but He did promise that He would always be there for us and that He would meet our every need.
There is a promise for every situation that we may face left on record for us in God's word. We, as born again believers are not exempt from problems, but we can face anything that comes our way, if we just trust Jesus.
God doesn't always take us out of every situation. Sometimes He allows us to go through something for a while. When He does, it's meant to build us up, not to tear us down. Regardless of the situation you may be facing right now, cast it at the feet of Jesus, and allow Him to work it out, His way!