Question 80328
y^6 + 9y^3 + 8 = 0
First, notice that y^6 = (y^3)^2.  So this is really a quadratic equation where the variable is y^3.  We can solve for y^3 by factoring:

(y^3 + 8)(y^3 + 1) = 0

Now, set both sets of parentheses equal to 0 and solve for y^3. 
This gives y^3 = -8 or y^3 = -1.  All you have to do now is take the cube root of both sides of both equations.  You will get y = -2 or -1.