For someone with single filing status, $39,375 is the top of the 0% rate bracket for 2019. For 2020 it's $40,000.
The tax rate that applies to the long-term capital gain is determined by your total taxable income, including the long-term gain. But it's based on taxable income, not gross income. (Taxable income is basically Adjusted Gross Income minus deductions.) And the gain is not necessarily all taxed at the same rate. If your taxable income crosses a bracket boundary, portions of the gain could be taxed at different rates. Here are two examples of how the tax on a long-term capital gain is calculated, using your "hypothetical numbers" as a starting point, and assuming your filing status is single. All the figures in these examples are for 2020.
You are assuming an Adjusted Gross Income (AGI) of $35,000 before adding the long-term capital gain. Suppose your long-term capital gain is $15,000. That makes your AGI $50,000 ($35,000 plus the $15,000 gain). The standard deduction for single filing status for 2020 is $12,400. Subtracting the $12,400 standard deduction from your $50,000 AGI gives you taxable income of $37,600. That's less than the $40,000 maximum for the 0% bracket, so your entire long-term capital gain of $15,000 would be taxed at 0%.
Now suppose we take the same example, but your long-term capital gain is $25,000. That makes your AGI $60,000. Subtracting the $12,400 standard deduction gives you taxable income of $47,600, which is over the $40,000 top of the 0% bracket. A portion of the gain still fits into the 0% bracket. Your taxable ordinary income is $22,600 ($35,000 minus the $12,400 standard deduction). The top of the 0% bracket, $40,000, minus the $22,600 ordinary income is $17,400. So there is room for $17,400 of capital gain in the 0% bracket. The rest of the long-term capital gain, $25,000 - $17,400 = $7,600 goes into the next higher bracket and will be taxed at the 15% rate.
Also keep in mind that most states do not have lower tax rates for long-term capital gains like the federal tax does. If you are in a state that has income tax, you may have to pay state tax on the entire capital gain.
