How to find longest palendromic substring?

Question

For example you have string, where you need to find longest palindromic(symmetrical) substring with the best Big-O, how would you do that?

Example 1

Input: s = "babad"
Output: "bab"
Explanation: "aba" is also a valid answer.

Here is my solution, but it is too slow for this type of problem.

public String longestPalindrome(String s) {
    if (s == null || s.length() == 0)
        return s;
    String longest = s.substring(0, 1);
    for (int i = 0; i < s.length(); i++) {
        if(s.length()-i <longest.length()/2)
            break;
        String oddPal = findLengthofPalindrome(s, i, i);
        if (longest.length() < oddPal.length()) {
            longest = oddPal;
        }

        String evenPal = findLengthofPalindrome(s, i, i + 1);
        if (longest.length() < evenPal.length()) {
            longest = evenPal;
        }
    }
    return longest;

}

private String findLengthofPalindrome(String s, int left, int right) {
    while (left >= 0 && right < s.length() && s.charAt(left) == s.charAt(right)) {
        left--;
        right++;
    }
    return s.substring(left + 1, right);
}