When Paul writes to the Romans, he is dealing with the problem of sin. Paul discusses sin from two aspects: (1) The source of sin is Satan's lies.(2) The solution to sin is Christ's death. In which will you choose to live? Choose well!
There is no sin where there is no law (Rom 4:15). We might mistake this to mean that God's law is the source of sin. Sin is not imputed where there is no law. But does Paul say "Until the law sin was NOT in the world"? No, he says, "Until the law sin WAS in the world" (Rom 5:13). No one is accused of sin until there is a law, but don't blame the law for the sin, because the potential to sin is there before the law appears, and the law is not the cause of that. Paul goes on to say that God's law makes sin abound (Rom 5:20). But that does not make it the source of sin.
Paul adds that where sin abounds, grace also abounds (Rom 5:20). So if we say God's law is the source of what it makes abound, we must say God's law is at once the source of grace and the source of sin! That is a contradiction.
Paul says, "By the law is the knowledge of sin" (Rom 3:20). He explains that later: "Sin through the commandment becomes exceedingly sinful" (Rom 7:13). Shopkeepers put their wares under everybody's noses to increase sales. But they also increase thefts, so they have signs stating that shoplifting is a crime and offenders will be prosecuted. They may create an opportunity in which theft increases, but they are not the source of the crime. Sin takes opportunity by God's law, but God's law is not the source of sin (Rom 7:7-8).
Our flesh is not the source of sin
Our bodies and their desires are not evil in themselves. Lust is in the heart not in the flesh, and the body is dishonoured by sin (Rom 1:24). Sin is not in doing what the body naturally wants to do, but in "leaving the natural use" for a perversion (Rom 1:27). Our fleshly bodies are intended by God to be "instruments of righteousness" which proves that they are not evil (Rom 6:13). An "instrument" --such as an ordinary pen for example-- can be used in a variety of ways, as an instrument of good, or as an instrument of evil. It is not itself the source of sin.
Adam is not the source of sin
Sin entered the world through Adam (Rom 5:14,19). He gets the blame although Eve sinned first, because Eve was deceived, but Adam was not deceived (1Tm 2:14). This does not excuse Eve, but it does lay the blame more fairly and squarely upon Adam, because he sinned when he knew better. So it is said that sin came through Adam. But that is not to say it came from him. He was the channel, not the source.
Satan is the source of sin
The devil's lies are the source of sin. The fall in the garden of Eden shows us the source. Adam sinned because Eve offered him the forbidden fruit. Eve sinned because the devil told her a lie which she believed. So the sin originated in the devil's lie. People sin when they exchange God's truth for the deceit of the debased mind of Satan (Rom 1:25,28).
Sin is living the lie, and and all sinners are, in that sense, liars (Rom 3:4). Some live the devil's lie after the similitude of Eve --they sin in ignorance, being deceived. Others live the devil's lie after the similitude of Adam --knowing full well that they are doing wrong. When we read the perverted behaviour described in Romans chapter one, we may think, "How horrible! I would never do that!" But they who do such things may be deceived, whereas you may sin in seemingly less repugnant ways, yet knowing fully that you err. Whose sin is worse? Think about it.
Paul "willed" to do the good law his mind delighted in. Yet he did not do what he "willed" to do. On the other hand, he did things which he "willed" not to do! (Rom 7:18-25). This is not an argument against willing to obey God's law. We ought to will to do good and shun evil. But that, on its own, is not the solution, as Paul discovered.
Asceticism is not the solution to sin
Asceticism is abstinence from various comforts and pleasures. Abstinence from sin is required of course, but we are thinking rather of abstinence from things which are not sin in themselves. The sin would be in excessive or perverted use. The sin would be not in use, but in abuse.
Paul is persuaded that "there is nothing unclean of itself" (Rom 14:14). He does not, for example, approve of fornication. But there is nothing unclean about sexual intercourse in itself. To engage in sexual intercourse in wedlock may be a better solution to sin than abstaining from it in celibacy.
Vegetarianism is another example. Paul describes the vegetarian as "weak in faith" (Rom 14:1-2). It is good, of course, to refrain from things which cause the weak to stumble (Rom 14:21). We do not argue against abstinence from things which people commonly abuse. We commend it. But we should not mistake it as the solution to sin.
Good works are not the solution to sin
Don't misunderstand this! Paul was thankful for people's obedience (Rom 6:17). He said it was our reasonable service to offer our bodies as a living sacrifice to God (Rom 12:1). He exhorted Christians not to be lagging in diligence (Rom 12:11). Good works are a good and essential thing. But in themselves they are not a solution, for all have sinned and fall short (Rom 3:23). No amount of good works can cover that up. That is no reason to neglect good works, but it is a reason to look beyond them for the solution to sin.
We will not be forgiven of our sins on the basis that we piled up enough good works to cancel out our sins. We will be forgiven because Christ died for us (Rom 3:24).
The Lord Jesus is the solution to sin
God set Jesus forth to be an atonement by his blood (Rom 3:24). There is "no condemnation" to those who are "in Christ" (Rom 8:1). We are saved from wrath through him and his shed blood (Rom 5:8).There's your solution to sin.