Since [tex]30x^3-5x^2-60x=5x(6x^2-x-12)[/tex], you have to find factors of polynomial [tex]6x^2-x-12[/tex].
For the polynomial [tex]6x^2-x-12[/tex]
[tex]D=(-1)^2-4\cdot6\cdot (-12)=1+288=289 \\ \sqrt{D}= \sqrt{289} =17 \\ x_{12}= \frac{-(-1)\pm 17}{2\cdot 6} [/tex].
[tex]x_1= \frac{1+17}{12}= \frac{18}{12} = \frac{3}{2} \\ x_1= \frac{1-17}{12}=-\frac{16}{12} =- \frac{4}{3}[/tex]
and
[tex]6x^2-x-12=6(x- \frac{3}{2} )(x- (-\frac{4}{3}) )=(2x-3)(3x+4)[/tex].
Then [tex]30x^3 - 5x^2 - 60x=5x(6x^2-x-12)=5x(2x-3)(3x+4)[/tex].
