Ik kan twee manieren bedenken, de ene met GROUP_CONCAT en de andere met subquery.
SELECT user_id, GROUP_CONCAT(installed_version) as all_patterns
FROM your_table
GROUP BY user_id
HAVING all_patterns REGEXP 'Pattern 1'
AND all_patterns REGEXP 'Pattern 2';
--
SELECT * FROM
(
SELECT user_id, installed_version FROM your_table
WHERE installed_version LIKE 'Pattern 1'
) as tmp
WHERE installed_version LIKE 'Pattern 2';