To solve the equation x^2021 + x^2022 + x^2023 = 0, we can factor out an x^2021 term:

x^2021(x^0 + x^1 + x^2) = 0

Since any number raised to the power of 0 is equal to 1, we have:

x^2021(1 + x + x^2) = 0

Now, we can set each factor equal to zero:

x^2021 = 0

This implies that x = 0 is a solution.

1 + x + x^2 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 1, and c = 1. Substituting these values into the quadratic formula:

x = (-1 ± √(1 - 4(1)(1))) / (2(1))
x = (-1 ± √(-3)) / 2

Since the discriminant (b^2 - 4ac) is negative, the quadratic equation has no real solutions. Therefore, the only solution to the equation x^2021 + x^2022 + x^2023 = 0 is x = 0.