We can start solving the solution to the polynomial given by factoring out 2x, getting:
[tex]2x(x^2+2x-15)=0[/tex]
The expression inside the parenthesis is a quadratic equation. By methods of factoring, we can rewrite this as:
[tex]\begin{gathered} 2x((x+5)(x-3))=0 \\ 2x(x+5)(x-3)=0 \end{gathered}[/tex]
Solving for the value of x that satisfies the polynomial given, we have:
[tex]\begin{gathered} 2x=0,x+5=0,x-3=0 \\ x=0,x=-5,x=3 \end{gathered}[/tex]
Hence, the solutions to the polynomial given are x = -5, 0, 3.
Answer: x = -5, 0, 3
