#### Answer

$x=\left\{ \dfrac{1}{2},\dfrac{3}{5}\right\}$

#### Work Step by Step

Using the properties of equality, the given expression is equivalent to
\begin{array}{l}\require{cancel}
3+10x^2=11x
\\\\
10x^2-11x+3=0
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
equation
}$
\begin{array}{l}\require{cancel}
10x^2-11x+3=0
\end{array} has $ac=
10(3)=30
$ and $b=
-11
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-5,-6
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
10x^2-5x-6x+3=0
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(10x^2-5x)-(6x-3)=0
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
5x(2x-1)-3(2x-1)=0
.\end{array}
Factoring the $GCF=
(2x-1)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(2x-1)(5x-3)=0
.\end{array}
Equating each factor to zero (Zero Product Property), and then isolating the variable, the solution is $
x=\left\{ \dfrac{1}{2},\dfrac{3}{5}\right\}
.$