There is so much in these 7 verses. They are very deep, filled with a depth of thought and meaning that is significant for the understanding of our faith. In fact it might surprise you to know all seven verses are just one Greek sentence. It is like Paul has been bursting with ideas that they have tumbled out connected in a series. In the midst of the flow are some concepts that require us to pause and reflect on them.
That is part of the difficulty in translating these verses. Note how the first two translations have handled it. The Amplified Bible has tried to break apart the concepts and convey those. The American Standard has stuck more closely to the original Greek and has preserved the flow from one thought to another. So one is made up of 6 sentences while the other has preserved the one Greek sentence and turned it into one sentence in English. To understand the whole you need to follow the logical connections. Do it now,
AMPlified Bible
But now the righteousness of God has been revealed independently and altogether apart from the Law, although actually it is attested by the Law and the Prophets, namely, the righteousness of God which comes by believing with personal trust and confident reliance on Jesus Christ (the Messiah). [And it is meant] for all who believe. For there is no distinction, since all have sinned and are falling short of the honor and glory which God bestows and receives. [All] are justified and made upright and in right standing with God, freely and gratuitously by His grace (His unmerited favor and mercy), through the redemption which is [provided] in Christ Jesus, whom God put forward [before the eyes of all] as a mercy seat and propitiation by His blood [the cleansing and life-giving sacrifice of atonement and reconciliation, to be received] through faith. This was to show God’s righteousness, because in His divine forbearance He had passed over and ignored former sins without punishment. It was to demonstrate and prove at the present time (in the now season) that He Himself is righteous and that He justifies and accepts as righteous him who has [true] faith in Jesus. Rom 3:21-26
American Standard Version
But now apart from the law a righteousness of God hath been manifested, being witnessed by the law and the prophets; even the righteousness of God through faith in Jesus Christ unto all them that believe; for there is no distinction; for all have sinned, and fall short of the glory of God; being justified freely by his grace through the redemption that is in Christ Jesus: whom God set forth to be a propitiation, through faith, in his blood, to show his righteousness because of the passing over of the sins done aforetime, in the forbearance of God; for the showing, I say, of his righteousness at this present season: that he might himself be just, and the justifier of him that hath faith in Jesus.
LITV
But now a righteousness of God has been revealed apart from Law, being witnessed by the Law and the Prophets, even the righteousness of God through faith of Jesus Christ toward all and upon all those believing; for there is no difference, for all sinned and fall short of the glory of God, being justified freely by His grace through the redemption in Christ Jesus, whom God set forth as a propitiation through faith in His blood, as a demonstration of His righteousness through the passing over of the sins that had taken place before, in the forbearance of God, for a demonstration of His righteousness in the present time, for His being just and justifying the one that is of the faith of Jesus.
NLT
But now God has shown us a way to be made right with him without keeping the requirements of the law, as was promised in the writings of Moses and the prophets long ago. We are made right with God by placing our faith in Jesus Christ. And this is true for everyone who believes, no matter who we are. For everyone has sinned; we all fall short of God’s glorious standard. Yet God, in his grace, freely makes us right in his sight. He did this through Christ Jesus when he freed us from the penalty for our sins. For God presented Jesus as the sacrifice for sin. People are made right with God when they believe that Jesus sacrificed his life, shedding his blood. This sacrifice shows that God was being fair when he held back and did not punish those who sinned in times past, for he was looking ahead and including them in what he would do in this present time. God did this to demonstrate his righteousness, for he himself is fair and just, and he makes sinners right in his sight when they believe in Jesus.
Now we will look at pulling it all together.
But now the righteousness of God has been manifested
                      apart from the law,
                             although the Law
                               and the Prophets bear witness to it
  even the righteousness of God
           through faith in Jesus Christ
                unto all them that believe;
                for there is no distinction;
                for all have sinned,
                      and fall short of the glory of God;
                           being justified freely by his grace
                                through the redemption
                                       that is in Christ Jesus:     Â
                                             whom God set forth
                                                  to be a propitiation,
                                through faith,
                                     in his blood,
                                to show his righteousness
                                because of the passing over of the sins
                                         done aforetime,
                                           in the forbearance of God;
                                for the showing/demonstration,
                                         of his righteousness
                                         at this present season:
                                that he might himself be just,
                                             and the justifier of him
                                                        that hath faith in Jesus.
Â
To follow this schema, take note of the layers in which the sentences and concepts appear to see the layering in the Greek sentence to see how the sentences and propositions are connected.
A successful man is one who can lay a firm foundation with bricks others have thrown at him.
Anon