solve 24x^3-52x^2-60x=0

The equation will have 3 roots, since the maximum order of
polynomial is 3.

We'll factorize by x and we'll
get:

x(24x^2 - 52x - 60) =
0

We'll set each factor as
zero:

x1 =
0

and

24x^2 - 52x - 60 =
0

We'll divide by 4:

6x^2 -
13x - 15 = 0

We'll apply the quadratic
formula:

x1 = [-b+sqrt(b^2 -
4ac)]/2a

x1 =
[13+sqrt(169+360)]/12

x1 =
(13+23)/12

x1 = 3

x2 =
(13-23)/12

x2 = -10/12

x2 =
-5/6

The roots of the equation are: {-5/6 , 0
, 3}.