In plain words
Dying in rajas, one is born among those attached to action; dying in tamas, one is born in deluded wombs.
Word for word
Having gone to dissolution in rajas, he is born among those attached to action; likewise, dissolved in tamas, he is born in deluded wombs.
रजसि प्रलयं गत्वा कर्मसङ्गिषु जायतेतथा प्रलीनस्तमसि मूढयोनिषु जायते
Other commentaries
The commentators
▸Bhagavadgītābhāṣyam· bhāṣya
रजसि गुणे विवृद्धे प्रलयं मरणं गत्वा प्राप्य कर्मसङ्गिषु कर्मासक्तियुक्तेषु मनुष्येषु जायते । तथा तद्वदेव प्रलीनः मृतः तमसि विवृद्धे मूढयोनिषु पश्वादियोनिषु जायते ॥ १५ ॥
In plain words
When rajas is the quality that has grown strong, a person who goes to dissolution — who dies — is born among those who cling to action: human beings, bound fast to their doing. And in exactly the same way, one who dissolves — who dies — when tamas has grown strong is born in deluded wombs: the wombs of animals and the rest.
Close to the Sanskrit
When the quality rajas has grown strong, having gone to dissolution — that is, having reached death — he is born among the action-clinging, that is, among human beings bound up with attachment to action. Likewise — just in that same way — one dissolved, that is, dead, when tamas has grown strong, is born in deluded wombs, that is, in the wombs of animals and the like.