The transformed equation of  $x^3-\frac{5}{2}{x}^2-\frac{7}{18}x+\frac{1}{108}=0$  by removing fractional coefficients, is

$f\left(x\right)=x^3-\frac{5}{2}{x}^2-\frac{7}{18}x+\frac{1}{108}=0$

The transformed equation to remove fractional coefficients in f(x)=0 is f(x/m)=0

 $m=2\times 3$ 

Transformed Equation  whose roots are multiplied by 6 is  $f\left(\frac{x}{6}\right)={\left(\frac{x}{6}\right)}^3-\frac{5}{2}{\left(\frac{x}{6}\right)}^2-\frac{7}{18}\left(\frac{x}{6}\right)+\frac{1}{108}=0\Rightarrow x^{\mathit{3}}-15x^2-14x+2=0$