Perhaps your credit score isn't good enough or you you don't meet the minimum criteria for the balance transfer card you want. In that case, there are a couple of options to consider as an alternative.
Still interested in what you could save? Compare balance transfer offers.
A planned approach
Consolidate debts with a loan
While they won't be interest-free, debt consolidation loans are a more structured way to get debt-free. These tend to have higher interest rates than you would get with a balance transfer card.
One of the major differences between debt consolidation and a balance transfer is that when you balance transfer to a new credit card, you get the introductory interest rate for a specified length of time. Once that period ends, whatever is left of the amount initially transferred will revert to a different rate (typically either the rate applied to purchases or cash advances).
The problem is that you could make the minimum repayment throughout the entire introductory period — and use the card for new spending — meaning you don't actually use it to get out of debt.
Debt consolidation loans have a fixed term, which means you know with certainty when the loan will be paid back. Assuming you don't take on new debt in the interim, once that loan has been repaid, you would be debt-free. They can be repaid over a longer period of time than the introductory rate on credit card balance transfers, which tends to be in the range of 12 - 24 months. Debt consolidation loans usually only have an application fee. However, the application fee can vary based on your credit worthiness.
Talk with your creditors
Negotiate your rate
Use the snowball method
This strategy focuses debt repayments on the most expensive debt first and paying it off as quickly as possible. With the debt repaid, you can focus your efforts on the next most expensive debt, now making larger repayments since you've freed up some cash. This can be repeated until you're out of debt.