Answer
The solutions are $-i, i,$ and $3$.
Work Step by Step
Group the first two terms together and the last two terms together to obtain:
$(x^3+x)+(-3x^2-3)=0$
Factor out the GCF in each group ($x$ in the first and $-3$) to obtain:
$x(x^2+1)+(-3)(x^2+1)$
Factor out the GCF of the expression ($x^2+1$) to obtain:
$=(x^2+1)[x+(-3)]
\\=(x^2+1)(x-3)$
Use the Zero Factor Property by equating each factor to zero, then solve each equation to obtain:
\begin{array}{ccc}
\\&x^2+1=0 &\text{or} &x-3=0
\\&x^2=-1 &\text{or} &x=3
\\&x=\pm\sqrt{-1} &\text{or} &x=3
\\&x=\pm i &\text{or} &x=3
\end{array}
Therefore, the solutions are $-i, i,$ and $3$.
