Big picture answer: Have you read the entire Old Testament and New Testament? Think of the many times the New Testament teachers like Jesus and Paul went way out of their way to explain to Jews that nobody could live up to the standard and be the perfect Jew -- it's only by grace. And all the times Paul wrote that it doesn't matter if you're circumcised, eat meat offered to idols, etc. IMHO, the combined beliefs of faith alone and grace alone are a quick summary of New Testament belief being different from Old Testament belief.
But if you're more inclined to pay attention to one-liner verses, here are some:
For God so loved the world, that He gave His only begotten Son, that whoever believes in Him shall not perish, but have eternal life. (John 3:16)
Truly, truly, I say to you, he who hears My word, and believes Him who sent Me, has eternal life (John 5:24) For this is the will of My Father, that everyone who beholds the Son and believes in Him will have eternal life (John 6:40)
I am the resurrection and the life; he who believes in Me will live even if he dies. (John 11:25)
Yes, many times over, in-depth and in a serious manner, as I'm sure you have. It is not a matter of not being knowledgeable of the contents of the Bible, but a difference of interpretation.
Jesus and Paul did indeed warn time and again the impossibility of being saved under the Jewish law. But since almost no Christian today believes that one could, that is not what is in dispute today. What is in dispute is whether our conduct (either bad or good) has any impact on our salvation. And, as you must know, both Jesus and St. Paul were very clear that it did.
I like those verses. If anybody is truly searching for the answer, it is in those verses.