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 {$-5,0,5$}.
