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To delete a node from a general-purpose tree, follow these steps:

1. Find the node to be deleted Traverse the tree and locate the node to be deleted. This can be done by using a depth-first search or a breadth-first search algorithm.

2. Determine the number of child nodes Once the node is found, determine the number of child nodes it has. If the node has no children, it can be deleted easily. If it has one child, the child can be promoted to take the place of the node being deleted. If it has two children, a more complex algorithm will be required.

3. Remove the node from the tree Once the appropriate action has been determined, remove the node from the tree. This involves updating the pointers of the parent of the node being deleted to replace the node with its child or children.

4. Rebalance the tree (if necessary) If the tree is a balanced tree such as an AVL tree or a red-black tree, rebalancing may be necessary to maintain its balance and keep its performance characteristics intact.

5. Free memory Finally, free the memory associated with the deleted node.