Chapter 0 - Section 0.6 - Solving Miscellaneous Equations - Exercises - Page 34: 8

$0, \pm 1$

$10x(x^{2}+1)^{4}(x^{3}+1)^{5}-10x^{2}(x^{2}+1)^{5}(x^{3}+1)^{4}=0$ $10x(x^{2}+1)^{4}(x^{3}+1)^{4}[(x^{3}+1)-x(x^{2}+1)]=0$ $10x(x^{2}+1)^{4}(x^{3}+1)^{4}(x^{3}+1-x^{3}-x)=0$ $-10x(x-1)(x^{2}+1)^{4}(x^{3}+1)^{4}=0$ $x=0, x=1, x=-1$