There is no single answer to this, and that is the part nobody tells you. The same balance at the same rate can take twelve years or fifty, depending purely on how your card calculates its minimum. This shows all three ways at once.
Search this question and you will find confident, specific answers that contradict each other. One reputable source says twenty years on a balance. Another says ten to fifteen on the same balance. A third says twenty-nine years, and a fourth says fifty-three.
None of them are wrong. They have each picked a different minimum-payment structure and then quoted the result as though it were the answer. The structure is doing all the work, and it usually goes unmentioned.
That matters because you do not get to choose the structure. Your card issuer picked it when you opened the account, and it is the single biggest factor in how long your debt lasts. Working out which one you have tells you more than any generic payoff estimate.
The reason minimums stretch so far is that the payment shrinks as the balance falls. You are always paying a percentage of a smaller number, so progress decelerates exactly when you need it to accelerate.
Fixing the payment breaks that. Pay the same amount every month rather than whatever the statement asks, and the timeline collapses, because every dollar of progress compounds instead of reducing next month's payment. On most balances a fixed payment set at today's minimum will clear the debt several times faster than following the minimum down.
The other lever is the rate itself. A balance transfer at a lower rate, or a personal loan used to consolidate, changes the arithmetic rather than just the effort. Whether that is worth it depends on the transfer fee and whether the balance is actually cleared before the promotional rate ends.