## Elementary Technical Mathematics

The factorized solution of the equation will be $3\left( \left( 5x-18 \right)\left( 2x+15 \right) \right)$.
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}