how would i sove this problem?

Question

x^6 + 3x^3 + 2 = 0

Answer 1

x^6+3x^3+2=0
It can also be written as:
(x^3)^2+3(x^3)+2=0...........(1)
Let a=(x^3), then we may rewrite equation (1) as:
a^2+3a+2=0
or,a^2+a+2a+2=0
or,a(a+1)+2(a+1)=0
or,(a+1)(a+2)=0
either,a=-1 or,a=-2
that is (x^3)=-1 or (x^3)=-2
Therefore, x=-1 or x=cube root of -2
this is the solution to your equation.