Answer
$x=\{ \pm i, 3 \}$
Work Step by Step
Using factoring by grouping, the given equation, $
10x^3+10x-30x^2-30=0
,$ is equivalent to
\begin{array}{l}\require{cancel}
(10x^3+10x)-(30x^2+30)=0
\\\\
10x(x^2+1)-30(x^2+1)=0
\\\\
(x^2+1)(10x-30)=0
.\end{array}
Equating each factor to zero, then,
\begin{array}{l}\require{cancel}
x^2+1=0
\\\\
x^2=-1
\\\\
x=\pm\sqrt{-1}
\\\\
x=\pm i
,\\\\\text{OR}\\\\
10x-30=0
\\\\
10x=30
\\\\
x=\dfrac{30}{10}
\\\\
x=3
.\end{array}
Hence, the solution set is $
x=\{ \pm i, 3 \}
.$
