Question

solve for x:

-x^6 - x^3 + 12 = 0

Answer 1

x^6 + x^3 - 12 = 0

x^3 = y

y^2 + y - 12 = 0
y^2 + 4y - 3y - 12 = 0
y(y+4)-3(y+4) = 0
(y+4)(y-3) = 0

replace y = x^3..

x^3 + 4 = 0
x^3 - 3 = 0

x^3 = -4
x^3 = 3

x = cuberoot(-4)
x = cuberoot(3)