Answer
Solutions:
$x=2$
$x=-1$
Work Step by Step
Notice that: $-7x^3=x^3-8x^3$
$x^6-7x^3-8=0$
$x^6+x^3-8x^3-8=0$
$x^3(x^3+1)-8(x^3+1)=0$
$(x^3-8)(x^3+1)=0$
$x^3-8=0$
$x^3=8$
$x=\sqrt[3] 8=2$
or
$x^3+1=0$
$x^3=-1$
$x=\sqrt[3] {-1}=-1$
Check the solutions:
$x=2$:
$2^6-7(2)^3-8=64-7(8)-8=64-56-8=0$
$x=-1$:
$(-1)^6-7(-1)^3-8=1-7(-1)-8=1+7-8=0$
