One partner buys out another = Schedule D for the selling partner. The partnership is not receiving or expensing any of the $40,000.
The exiting partner should not have any equipment, it should be owned by the partnership.
The exiting partner may have goodwill, but the partnership should really own the goodwill of the business.
You may find https://www.irs.gov/newsroom/questions-and-answers-about-technical-terminations-internal-revenue-cod... of interest.

The simple version is:

Old partner (selling partner) has a gain or maybe a loss on the $ 40,000 received.

New partner (buying partner) has $ 40,000 *outside basis*.

The partnership reflects the change in ownership by issuing part year K-1 to the old partner & the new partner (unless all this happens tonight at the stroke of midnight...)

so basically the entering partner cannot deduct the $40k  ?  

It is like the new partner bought some stock in Uber. He deducts it when he sells, adjusted for changes to basis from the partnership.

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@jbdaigle1102 wrote:

so basically the entering partner cannot deduct the $40k  ?  

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Correct, the entering partner does not get a deduction for his 40k investment until he disposes of the investment.