Consulta SQL para seleccionar pares de valores en una columna 1 que coincidan con uno de los dos patrones en la columna 2

Se me ocurren dos formas, una con GROUP_CONCAT y la otra usando subconsulta.

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';