Chapter 5 - Section 5.7 - Polynomial Equations and Their Applications - Exercise Set - Page 390: 45

$0,-3,-5$

Given: $2x^3+16x^2+30x=0$ or, $2x(x^2+8x+15)=0$ Need to use factorization to solve the quadratic equation. This can be factorized as follows: $2x^2(x^2+3x+5x+15)=0$ or, $2x^2(x+3)(x+5)=0$ Set each factor equal to zero, we get Now, $2x^2=0 \implies x=0$ Also, $x+3=0$, and $x+5=0$ Thus, $x=0,-3,-5$