Verses with the word carefulness in the New Testament (2 verses):

1 Corinthians 7:32
But I would have you without carefulness. He that is unmarried careth for the things that belong to the Lord, how he may please the Lord:

2 Corinthians 7:11
For behold this selfsame thing, that ye sorrowed after a godly sort, what carefulness it wrought in you, yea, what clearing of yourselves, yea, what indignation, yea, what fear, yea, what vehement desire, yea, what zeal, yea, what revenge! In all things ye have approved yourselves to be clear in this matter.