The regular expression:

(?-imsx:=(?:"[^"']+")|(?:'[^"']+'))

matches as follows:
  
NODE                     EXPLANATION
----------------------------------------------------------------------
(?-imsx:                 group, but do not capture (case-sensitive)
                         (with ^ and $ matching normally) (with . not
                         matching \n) (matching whitespace and #
                         normally):
----------------------------------------------------------------------
  =                        '='
----------------------------------------------------------------------
  (?:                      group, but do not capture:
----------------------------------------------------------------------
    "                        '"'
----------------------------------------------------------------------
    [^"']+                   any character except: '"', ''' (1 or
                             more times (matching the most amount
                             possible))
----------------------------------------------------------------------
    "                        '"'
----------------------------------------------------------------------
  )                        end of grouping
----------------------------------------------------------------------
 |                        OR
----------------------------------------------------------------------
  (?:                      group, but do not capture:
----------------------------------------------------------------------
    '                        '\''
----------------------------------------------------------------------
    [^"']+                   any character except: '"', ''' (1 or
                             more times (matching the most amount
                             possible))
----------------------------------------------------------------------
    '                        '\''
----------------------------------------------------------------------
  )                        end of grouping
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------