Question 4359
 Step I) Try to factor out (x-3)
 5x^3-36x^2+189=0 
  i) Separate  -36x^2 into two terms:
    5x^3- 15x^2 - 21x^2 + 189=0 ,
  ii)Regrouping :
    5x^2(x -3) - 21(x^2 - 9) = 0
  iii) Note (x^2 -9) = (x-3)(x+3) [a formula you should know.]
    5x^2(x -3) - 21(x-3)(x+3) = 0
  iv) Factor out (x-3):
    (x-3)[5x^2 -21(x+3)] = 0,
  Or  (x-3)[5x^2 -21 x -63] = 0.

 Step II:
 x - 3 = 0 implies x = 3
 By quadratic formula on 5x^2 -21 x -63 = 0 
 we have x = [21 + sqrt(21^2 + 20 * 63)]/10 
           = [21 + 9 sqrt(21)]/ 10 (or 3/10[ 7 + 3 sqrt(21)])
or x = [21 - 9 sqrt(21)]/ 10
  
 Kenny