Answer
The required solution is $\left\{ -\frac{1}{2},2 \right\}$
Work Step by Step
The expression can be calculated as provided below:
$\begin{align}
& 2\left( 1-{{u}^{2}} \right)+3u=0 \\
& 2-2{{u}^{2}}+3u=0
\end{align}$
Then, multiply the equation by -1 and rearrange it:
$\begin{align}
& -2+2{{u}^{2}}-3u=0 \\
& 2{{u}^{2}}-3u-2=0
\end{align}$
And split the middle term as given below:
$\begin{align}
& 2{{u}^{2}}-3u-2=0 \\
& 2{{u}^{2}}+u-4u-2=0 \\
& u\left( 2u+1 \right)-2\left( 2u+1 \right)=0 \\
& \left( 2u+1 \right)\left( u-2 \right)=0
\end{align}$
Then, find the possible values of $u$:
$\begin{align}
& 2u+1=0 \\
& 2u=-1 \\
& u=-\frac{1}{2}
\end{align}$
And,
$\begin{align}
& u-2=0 \\
& u=2
\end{align}$
Thus, the possible values are $-\frac{1}{2}$ and $2$.
