BhG 3.20

syntax

janakādayaḥ (Janaka and others) karmaṇā eva hi (merely by activity) saṁsiddhim (perfection) āsthitāḥ (those who attained).
[tvaṁ] (you) loka-saṅgraham eva api (even the welfare of the world) saṁpaśyan (considering) [karma] (activity) kartum (to do) arhasi (you should).

grammar

karmaṇā	–	karman 3n.1 n. – by activity (from: √kṛ – to do);
eva	–	av. – certainly, just, merely;
hi	–	av. – because, just, indeed, surely;
saṁsiddhim	–	sam-siddhi 2n.1 f. – accomplishment, fulfilment, perfection, success (from: √sidh – to succeed, to become perfect);
āsthitāḥ	–	āsthita (ā-√sthā – to resort, to go towards) PP 1n.3 m. – those who resorted to, who attained;
janakādayaḥ	–	janaka-ādi 1n.3 m. – Janaka and others (from: √jan – to be born, to produce, jana – creature, race, janaka – progenitor, the king of Videha, Sītā’s father; ādi – suffix: beginning with, etc.);
loka-saṁgraham	–	loka-saṁgraha 2n.1 m.; lokānāṁ saṅgraham iti – protection of the world (from: loka – world; sam-√grah – to hold together, to support, saṁ-graha – holding together, collection, protection);
eva	–	av. – certainly, just, merely;
api	–	av. – although, moreover, besides, even;
saṁpaśyan	–	saṁpaśyant (sam-√dṛś – to see completely, to consider) PPr 1n.1 m. – [while] considering;
kartum	–	√kṛ (to do) inf. – to do;
arhasi	–	√arh (to deserve, to be able to) Praes. P 2v.1 – you deserve;

textual variants

karmaṇaiva → karmaṇeva (as if by activity);

Śāṃkara

The key:
an excerpt from the commented verse
quotes from the scriptures
starting polemic

The wise should set an example to the masses. For the following reason also (shouldst thou perform action):		yasmāc ca —
By action only, indeed, did Janaka and others try to attain perfection. Even with a view to the protection of the masses thou shouldst perform (action).		karmaṇaiva hi saṃsiddhim āsthitā janakādayaḥ | loka-saṃgraham evāpi saṃpaśyan kartum arhasi ||3.20||
The wise kshatriyas of old, such as Janaka and Aśvapati tried by action alone to attain moksha (samsiddhi).		karmaṇaiva hi yasmāt pūrve kṣatriyāḥ vidvāṃsaḥ saṃsiddhiṃ mokṣaṃ gantum āsthitāḥ pravṛttāḥ | ke? janakādayaḥ janakāśvapati-prabhṛtayaḥ |
If they were persons possessed of right knowledge, then we should understand that, since they had been engaged in works they tried to reach moksha with action, i. e., without abandoning action, with a view to set an example to the world. If, on the other hand, such men as Janaka were persons who had not attained right knowledge, then, (we should understand), they tried to attain moksha through action which is the means of attaining purity of mind (sattva-suddhi).		yadi te prāpta-samyag-darśanāḥ, tataḥ loka-saṃgrahārthaṃ prārabdha-karmatvāt karmaṇā sahaivāsaṃnyasyaiva karma saṃsiddhim āsthitā ity arthaḥ | athāprāpta-samyag-adarśanāḥ janakādayaḥ, tadā karmaṇā sattva-śuddhi-sādhana-bhūtena krameṇa saṃsiddhim āsthitā iti vyākhyeyaḥ ślokaḥ |
If you think that obligatory works were performed by the ancients such as Janaka because they were ignorant, and that it does not follow from that fact alone that action should be performed by another who possesses right knowledge and has done all his duties, – even then, as subject to your prarabdha-karma (the karma which has led you to this birth as a kshatriya), and having regard also to the purpose of preventing the masses from resorting to a wrong path, you ought to perform action.		atha manyase pūrvair api janakādibhiḥ ajānadbhir eva kartavyaṃ karma kṛtam | tāvatā nāvaśyam anyena kartavyaṃ samyag-darśanavatā kṛtārtheneti | tathāpi prārabdha-karmāyattaḥ tvaṃ loka-saṃgraham evāpi lokasya unmārga-pravṛtti-nivāraṇaṃ loka-saṃgrahaḥ, tam evāpi prayojanaṃ saṃpaśyan kartum arhasi ||3.20||

Rāmānuja

commentary under the verse BhG 3.21

Śrīdhara

atra sadācāraṃ pramāṇayati karmaṇaiveti | karmaṇaiva śuddha-sattvāḥ santaḥ saṃsiddhiṃ samyag-jñānaṃ prāptā ity arthaḥ | yadyapi tvaṃ samyag-jñāninam evātmānaṃ manyase, tathāpi karmācaraṇaṃ bhadram evety āha loka-saṅgraham ity ādi | lokasya saṅgrahaṃ sva-dharme pravartanam | mayā karmaṇi kṛte janaḥ sarvo ‚pi kariṣyati | anyathā jñāni-dṛṣṭāntenājño nija-dharmaṃ nityaṃ karma tyajan patet | ity evaṃ loka-rakṣaṇam api tāvat prayojanaṃ saṃpaśyan kathaṃ kartum evārhasi | na tyaktum ity arthaḥ

Madhusūdana

nanu vividiṣor api jñāna-niṣṭhā-prāpty-arthaṃ śravaṇa-manana-nididhyāsanānuṣṭhānāya sarva-karma-tyāga-lakṣaṇaḥ saṃnyāso vihitaḥ | tathā ca na kevalaṃ jñānina eva karmānadhikāraḥ kintu jñānārthino ‚pi viraktasya | tathā ca mayāpi viraktena jñānārthinā karmāṇi heyāny evety arjunāśaṅkāṃ kṣatriyasya saṃnyāsānadhikāra-pratipādanenāpanudati bhagavān karmaṇaiveti |

janakādayo janakā-jāta-śatru-prabhṛtayaḥ śruti-smṛti-prasiddhāḥ kṣatriyā vidvāṃso ‚pi karmaṇaiva saha na tu karma-tyāgena sa saṃsiddhiṃ śravaṇādi-sādhyāṃ jñāna-niṣṭhām āsthitāḥ prāptāḥ | hi yasmād evaṃ tasmāt tvam api kṣatriyo vividiṣur vidvān vā karma kartum arhasīty anuṣaṅgaḥ | brāhmaṇaḥ putraiṣaṇāyāś ca vittaṣaṇāyāś ca lokaiṣaṇāyāś ca vyutthāyātha bhikṣācaryaṃ caranti iti saṃnyāsa-vidhāyake vākye brāhmaṇatvasya vivakṣitatvāt | svārājya-kāmo rājā rāja-sūyena yajeta ity atra kṣatriyatvāvat | catvāra āśramā brāhmaṇasya trayo rājan yasya dvau vaiśyasya iti ca smṛteḥ | purāṇe ‚pi –

mukhajānāmayaṃ dharmo yad viṣṇor liṅga-dhāraṇam |
bāhu-jātoru-jātānām nāyaṃ dharmaḥ praśasyate ||

iti kṣatriya-vaiśyayoḥ saṃnyāsābhāva uktaḥ | tasmād yuktam evoktaṃ bhagavatā karmaṇaiva hi saṃsiddhim āsthitā janakādayaḥ |

sarve rājāśritā dharmā rājā dharmasya dhārakaḥ ity ādi smṛter varṇāśrama-pravartakatvenāpi kṣatriyo ‚vaśyaṃ karma kuryād ity āha loketi | lokānāṃ sve sve dharme pravartanam unmārgān nivartanaṃ ca loka-saṅgrahas taṃ paśyann api-śabdāj janakādi-śiṣṭācāram api paśyan karma kartum arhasy evety anvayaḥ | kṣatriya-janma-prāpakeṇa karmaṇārabdha-śarīras tvaṃ vidvān api janakādivat prārabdha-karma-phalena loka-saṅgrahārthaṃ karma kartuṃ yogyo bhavasi na tu tyaktuṃ brāhmaṇa-janmālābhād ity abhiprāyaḥ | etādṛśa-bhagavad-abhiprāya-vidā bhagavatā bhāṣya-kṛtā brāhmaṇasyaiva saṃnyāso nānyasyeti nirṇītam | vārtika-kṛtā tu prauḍhi-vāda-mātreṇa kṣatriya-vaiśyayor api saṃnyāso ‚stīty uktam iti draṣṭavyam

Viśvanātha

atra sadācāraṃ pramāṇayati karmaṇeti | yadi vā tvam ātmānaṃ jñānā̆dhikāriṇaṃ manyase, tad api loke śikṣā grahaṇārthaṃ karmaiva kurv ity āha loketi

Baladeva

sadācāram atra pramāṇayati karmaṇaiveti | karmaṇaivopāyena viśuddha-cittāḥ santaḥ saṃsiddhiṃ svātmāvalokana-lakṣaṇām āsthitāḥ prāpuḥ | karmaṇaiveti viśeṣaṇa-sambandha eva-kāras tasyāyogaṃ vyavacchinnatti śaṅkha-pāṇḍura evetivat | tena śravaṇāder na vyudāsaḥ | karmaṇā yajñādinā sahaiva śravaṇādineti kecit |

nanu saniṣṭhasyātmāvalokane karmānuṣṭhānaṃ nāstīty uktam | mama pariniṣṭhitasyāvalokita-sva-parātmanaḥ karmopadeśaḥ kuta iti cet tatrāha loketi | satyaṃ tvam īdṛśa eva tathāpi loka-saṅgrahāya karma kurv iti arjune mayi karma kurvāṇe sarva-lokaḥ karma kariṣyati | itarathā mad-dṛṣṭāntenājño ‚pi lokaḥ karma tyajan patiṣyatīti loka-saṃrakṣaṇaṃ tat phalam