What is the solution of the equation?

3 ^2sqrt (x + 2)^3 + 3 = 27

I will assume you meant:

3 ^ (2√ ((x + 2)^3 + 3) = 27

3 ^ (2√ ((x + 2)^3 + 3) = 3^3
2√ ((x + 2)^3 + 3 = 3
2√(x+2)^3 = 0
x+2 = 0
x = -2