The Knowledge of Sin
"Now we know that what things soever the law saith, it saith to them who are under the law: that every mouth may be stopped, and all the world may become guilty before God." - Romans 3:19
In Romans Chapter 3, Paul finalizes his case against humanity. Humanity is lost, and helplessly stuck in sin. God had given a law to Israel and Israel had failed to keep it, and not only they, but the world. Thus, the entire world could be shown guilty by the standard of the law.
If things stopped here, humanity has no hope. Humanity doesn't desire God, doesn't want God, and God could have just let us end in our own self destruction; wallowing in our sin.
The Long Suffering of God
"Howbeit for this cause I obtained mercy, that in me first Jesus Christ might shew forth all longsuffering, for a pattern to them which should hereafter believe on him to life everlasting." - 1 Timothy 1:16
God is not willing that any should perish. Instead of judging the world now, God is choosing to not impute their trespasses. This means that God today is waiting. Waiting for you to trust not in what you have done, but in what he did.
God desires that we all have faith and trust in the crosswork of Christ to be saved from eternal salvation and saved to our God given purpose.
By Grace Through Faith
"...For if through the offence of one many be dead, much more the grace of God, and the gift by grace, which is by one man, Jesus Christ, hath abounded unto many." - Romans 5:15
Just like Adam had sinned and brought sin and death to all of humanity, Jesus Christ resurrected from the dead and brought with him life made available to all of humanity. In this act, Jesus Christ paid the penalty for our sins, and God has offered this by grace through faith.
Do you believe solely in Christ's death, burial, and resurrection as a payment for your sins? If so, then you've found the solution to your sin problem.