To solve the equation, we can start by subtracting 64 from both sides:

(2x + 1)^3 = -64

Next, we can take the cube root of both sides to eliminate the exponent:

∛((2x + 1)^3) = ∛(-64)

Simplifying the cube root of -64 gives us:

2x + 1 = -4

Now, we can subtract 1 from both sides:

2x = -4 - 1

2x = -5

Finally, we divide both sides by 2 to solve for x:

x = -5/2

Therefore, the solution to the equation (2x + 1)^3 + 64 = 0 is x = -5/2.