# Chapter 5 - Section 5.8 - Solving Equations by Factoring and Problem Solving - Exercise Set - Page 323: 42

$\{0,6,9\}$

#### Work Step by Step

$-2t^{3}=108t-30t^{2}$ $-2t^{3}-108t+30t^{2}=0$ $-2t^{3}+30t^{2}-108t=0$ Factor out the GCF, $-2t$ $-2t(t^{2}-15t+54)=0$ Factoring the equation. $-2t(t-9)(t-6)=0$ Setting each factor to zero. $-2t = 0$ $t= 0$ OR $t-9=0$ $t=9$ OR $t-6=0$ $t=6$ Solution set is $\{0,6,9\}$

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