CA landlord tenant law, landlord gave 3 day notice, accepts partial payment, gives 3 day notice

Well it depends, If you paid a partial amount of your rent after the landlord posted the first 3-day notice and the landlord accepted the rent, then that may constitute a waiver of the notice. This is useful because in unlawful detainer (eviction) actions in California a landlord must precisely state the amount of rent owed. If you have proof of payment drawn up after the first three-day notice, then you can argue that the Landlord has not precisely stated the rent owed. If the landlord does not state the precise amount owed you can file a demurrer to an unlawful detainer complaint based on uncertainty. This can drag out the legal process for an eviction and frustrate the landlord. If you're still behind on your rental payments even after the partial payment the landlord can still evict you. The landlord just needs to serve another 3-day notice with the new amount. Long story short, yes, they can still seek to evict you if you only made a partial payment, they just have to start over and precisely state the amount of rent past due.

Actually, you need to read the notice carefully. Many notices state acceptance of partial rent does not constitute a waiver. In that case, they will be able to proceed...

In California, if a tenant accepts rent for less than the amount stated in the 3 Day Notice during or after the 3 Day period, the 3 Day Notice is waived, and a new one will have to be served before an unlawful detainer action can be filed.

Sorry, in California, if a landlord or landlord's agent accepts rent for less than the amount stated in the 3 Day Notice during or after the 3 Day period, the 3 Day Notice is waived, and a new one will have to be served before an unlawful detainer action can be filed.