Understand the differences in results, but do not be dominated by them.

If Arjuna does not desire the kingdom, nor heaven, then for what purpose should he fight? Krishna teaches that one should see joy and sorrow, gain and loss, victory and defeat as equal, and perform actions as a duty, regardless of the outcome.

To see things equally does not mean that the differences in results become unclear. It means letting go of attachment to desirable outcomes and aversion to undesirable ones, so that neither dominates your mind. The key to preventing actions from becoming constraints lies in maintaining balance even amidst gains and losses, or wins and defeats.

Japanese Translation from the Geeta Press Edition - Chapter 2, Section 38: "Seeing Joy and Suffering, Gain and Loss, Victory and Defeat as Equal."

In the previous section, the speaker mentioned that participating in the battle would bring rewards such as ruling on earth or reaching heaven. However, Arjuna had previously stated that he did not want to destroy his own family, even for the sake of earthly dominion or sovereignty over the three realms. Therefore, the next section will explain how one should participate in the battle out of a sense of duty, without seeking the pleasures of kingship or the joys of heaven.

Sanskrit original text

सुखदुःखे समे कृत्वा लाभालाभौ जयाजयौ ।
ततो युद्धाय युज्यस्व नैवं पापमवाप्स्यसि ॥ ३८ ॥

Romanization

sukha-duḥkhe same kṛtvā lābhālābhau jayājayau |
tato yuddhāya yujyasva naivaṃ pāpam avāpsyasi || 38 ||

Victory and defeat, gain and loss, joy and suffering – see them as equal. Then prepare for battle. If you fight in this way, you will not incur sin. (38)

To not make distinctions in the heart between victory and defeat, gain and loss, joy and suffering that may result from a battle. In other words, to not have attachments or resistance, nor feelings of joy or sorrow towards them. This is what it means to "regard joy and suffering as equal."

The Lord is saying the following: To Arjuna, He commands to prepare for battle. If Arjuna truly does not seek the pleasures of kingship or the joys of heaven, even in that case, he must completely abandon the sense of differentiation regarding the results of the battle. And with such an equal-mindedness, one should engage in war as a duty. A battle conducted with this spirit will bring about eternal and ultimate peace.

Furthermore, the Lord points out that if Arjuna fights with his mind, he will not incur sin.

This is a response to the argument that stopping the battle would be justified because killing one's own family members constitutes a sin (I.36, 39, 45).

Here, the Lord clearly indicates that if Arjuna cultivates an attitude of equanimity towards joy and suffering, victory and defeat, etc., in other words, if he participates in battle with indifference to its outcome, then he will not even touch a trace of sin.

And he will also be liberated from the bonds of actions that take the form of reward and punishment.