Your debt consolidation credit report should look better than the credit report you had before you combined your bills.
Even though debt consolidation creates a new credit account, lenders consider the other accounts as paid in full.
Timely repayment of new credit will also have a positive effect on your credit in the long term.
It is important to keep up with your debt consolidation loan payments, and any other credit payments that you are required to make, otherwise your score will drop.
Closing credit card accounts after you have consolidated the debt can negatively impact your score.
It is better to borrow against your equity line, than it is to apply for new credit cards repeatedly in order to take advantage lower interest rates.