Righteousness Accounted or Worked For - Quick & Clear Bible Study

Is righteousness accounted to a person when he believes in Jesus as his Savior or is work needed to have righteousness? Some verses, such as Romans 3:22, sound like righteous is accounted while some verses, like 2 Timothy 2:22, as if righteousness is worked for.

Verses used in this Bible study:
Romans 3:21-28
Romans 4:3-6
2 Corinthians 5:21
Philippians 3:9
Revelation 19:7,8
Luke 1:5,6
2 Timothy 2:22
2 Timothy 3:16
Hebrews 11:32-34