[D]:  " x = 0, -3, 5/2 "  .
{Assuming:  " 2x³ + x²  − 15x = 0 ".}.
Explanation:
Given:
   2x³ + x² − 15x ;
Â
    →  (2x³ + x²) − 15x ;
 Â
     →   2x³ + x² − 15x  =   x * (2x² + x − 15) ;
    Â
     →  Factor the expression:  "(2x² + x − 15)" ;
                  Â
       → (2x² + x − 15) = Â
      Â
      →  2x² − 5x + 6x − 15 ;
      → Add the "first TWO (2) terms", and pull out the "like factors" ;                     →  x*(2x − 5) ;
      →  Add the "last TWO (2) terms, pulling out "common factors";
              →  3*(2x − 5) ;
      →  Now, add up the previous FOUR (4) terms; to get:
              → (x + 3)(2x − 5) ; Â
      → Now, we have factored the:
          "(2x² + x − 15)" of:  " x*(2x² + x − 15) " ;Â
      → So we add the "x"; and write the entire factored expression:
           →  x*(x + 3)(2x − 5) ;     Â
Now, assume the question is asking to solve for "x" by factoring;
  when the expression is "equal to zero" ;
That is, when: Â
        →  x*(x + 3)(2x − 5) = 0 ;
Since we have THREE (3) multiplicands; Â and anything times "0" equals "0" ;
  this equation holds true when:
 1) x = 0 ;
 2) (x + 3) = 0 ;
 Â
Subtract "3" from each side of the equation;
  x + 3 − 3 = 0 − 3 ;Â
 Â
     x = -3 ;Â
3)  2x − 5 = 0 ;Â
Add "5" to each side of the equation;
2x − 5 + 5 = 0 + 5 ;
2x = 5 ; Now, divide EACH side of the equation by "2" ; to isolate "x" on one side of the equation; and to solve for "x" ;Â
2x/2 = 5/2 ;
x = 5/2; or, write as 2.5; or write as 2½ .
Put simply, the equation is true when:
  x = 0, -3, 5/2 ;  which is: Answer choice: [D].