You might. First of all, the lower tax rates and the 0% bracket apply only to long-term capital gain. Short-term capital gains are taxed the same as earned income or any other ordinary income.
The tax brackets for long-term capital gains apply to your total taxable income, including both earned income and the capital gain. Note that it is based on taxable income, not gross income.
Here's an example. Suppose you are single and you have $35,400 of wages and a $20,000 capital gain. Your total income is $55,400. After subtracting the $12,400 standard deduction your taxable income is $43,000. Since your total taxable income is over $40,000, you will pay 15% tax on $3,000 of the capital gain.
