Question 1013724
The easiest way is to graph it and the parts of the graph below 0 are what is desired.  This then allows one to look for specific factors to finish the work.

{{{graph(300,200,-10,10,-10,50,9x^3-18x^2-25x+50)}}}
(x-2) appears to be a factor of the equation equaling 0. x=2
substitute 2 into the equation and this equals 0, so it is not a solution, but allows us to factor (x-2) out of the equation.  Using synthetic or long division, the remaining factor is 9x^2-25, which is a difference of squares.
The other two roots are +/-(5/3).  That is because (3x-5)(3x+5)=0 and solving for x will give +/- (5/3)
It is less than 0 between ((5/3),2) and it is less than 0 between (-oo,(5/3))
{{{graph(300,200,-2,4,-10,10,9x^3-18x^2-25x+50)}}}