Are there investors involved?
Do you have a Board of Directors? If so, have they been notified?
What does your operating agreement state would be the required processes upon the dissolution of the LLC?
What are you options stated on the operating agreement?
Can you sell your percentage of the LLC to your partner?
Can you resign your partnership?
Is there a substantial amount of money involved?
Do not take it upon yourself to dissolve the LLC if your partner is not in total agreement.
Make sure you are totally indemnified from any civil and or criminal liabilities, and obtain a clearance certificate from the state and the federal government for any and all tax liabilities. (Discuss this section with your CPA, if you have one, if not, find one).
I do not know your complete circumstance, so with the information you have provided, the best thing you can do is contact a professional business attorney. Let him/her help you.
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As you said, you and your husband are getting a divorce and instead of giving half the business, either of them should keep it. Whoever wants to keep it, he should pay 60% of the amount of his business to others. Then you or your husband should start your new business. Both of you know how to do business, then you can start it afresh.