небре́жный — meaning in English

nebrezhnyy

English meaning

blithe adj Showing a careless or casual disregard for something serious.
careless adjective Not paying enough attention, so that mistakes or accidents happen.
casual adj Relaxed and informal, especially in style, manner, or dress.
jaunty adj Lively, confident, and stylish in manner or appearance.
lax adj Not strict or careful; loose in standards or discipline.
mindless adj Done without thought, purpose, or care.
nonchalant adjective Calm, relaxed, and seemingly unbothered by something that might normally cause concern.
perfunctory adj Done just to satisfy a basic requirement, without real care or effort.
remiss adj Careless or negligent about a duty or responsibility.
slack adj Loose; not pulled tight.
slapdash adj Done quickly and without much care or planning.
slipshod adj Careless and messy, done without enough care or attention.
sloppy adj Careless, messy, or lacking neatness or precision.
slovenly adj Untidy in appearance.

небре́жный is used for these senses in English:

blithe Casually careless or indifferent; showing a lack of concern; nonchalant.
careless Not giving sufficient attention or thought, especially concerning the avoidance of harm or mistakes. [from 16thc.]
casual Careless.
jaunty Ostentatiously self-confident.
lax Lacking care; neglectful, negligent.
mindless Heedless.
nonchalant Casually calm and relaxed.
nonchalant Indifferent; unconcerned; behaving as if detached.