Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 6 - Factoring, Solving Equations, and Problem Solving - Chapter 6 Test: 20

Answer

{$-5,0,5$}

Work Step by Step

Since $3x$ is common to both the terms of the equation, we take it out as a common factor: $3x^{3}=75x$ $3x^{3}-75x=0$ $3x(x^{2}-25)=0$ We simplify the expression further using the rule $a^{2}-b^{2}=(a+b)(a-b)$: $3x(x^{2}-25)=0$ $3x(x^{2}-5^{2})=0$ $3x(x+5)(x-5)=0$ Now, we equate all of the factors to zero to solve the equation: $3x(x+5)(x-5)=0$ $3x=0$ or $x+5=0$ or $(x-5)=0$ $x=0$ or $x=-5$ or $x=5$ Therefore, the solution set is {$-5,0,5$}.
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