Determine the roots of the cubic equation: $-5 x^{3}-5 x^{2}+210 x$

Step 1 ：We are given the cubic equation \(-5 x^{3}-5 x^{2}+210 x = 0\).

Step 2 ：To find the roots of the equation, we need to set the equation equal to zero and solve for x.

Step 3 ：The equation can be simplified by factoring out common factors. The factored form of the equation is \(-5x(x - 6)(x + 7) = 0\).

Step 4 ：The roots of the equation are the values of x that make the equation equal to zero.

Step 5 ：Setting each factor equal to zero gives us the roots of the equation: \(x = 0\), \(x - 6 = 0\) (which gives \(x = 6\)), and \(x + 7 = 0\) (which gives \(x = -7\)).

Step 6 ：Final Answer: The roots of the equation are \(\boxed{-7}\), \(\boxed{0}\), and \(\boxed{6}\).