We can use distribution property to multiply the polynomial by the monomial.
$$ \begin{aligned} \color{blue}{-5x} \cdot \left( -6x^2+1 \right) &= \color{blue}{-5x} \cdot \left( -6x^2\right) + \color{blue}{-5x} \cdot 1 = \\ &= 30x^3-5x \end{aligned} $$