Answer
The factorized solution of the equation will be $3\left( \left( 5x-18 \right)\left( 2x+15 \right) \right)$.
Work Step by Step
Take out the $3$ common term from the equation,
$30{{x}^{2}}+117x-810=3\left( 10{{x}^{2}}+39x-270 \right)$
Factorize the equation,
$\begin{align}
& 30{{x}^{2}}+117x-810=3\left( 10{{x}^{2}}+39x-270 \right) \\
& =3\left( 10{{x}^{2}}+39x-270 \right) \\
& =3\left( 10{{x}^{2}}+75x-36x-270 \right)
\end{align}$
Further simplify the equation:
$\begin{align}
& 30{{x}^{2}}+117x-810=3\left( 5x\left( 2x+15 \right)-18\left( 2x+15 \right) \right) \\
& =3\left( \left( 5x-18 \right)\left( 2x+15 \right) \right)
\end{align}$
