Elementary Technical Mathematics

Published by Brooks Cole
ISBN 10: 1285199197
ISBN 13: 978-1-28519-919-1

Chapter 16 - Cumulative Review - Page 568: 10


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: $\begin{align} & 30{{x}^{2}}+117x-810=3\left( 5x\left( 2x+15 \right)-18\left( 2x+15 \right) \right) \\ & =3\left( \left( 5x-18 \right)\left( 2x+15 \right) \right) \end{align}$
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