Chapter 7 - Polynomial Equations and Factoring - 7.4 - Solving Polynomial Equations in Factored Form - Exercises - Page 381: 6

$v=0$ and $v=-1$.

The given equation is $\Rightarrow -2v(v+1)=0$ Use zero-product property rule. $\Rightarrow -2v=0$ or $v+1=0$ Solve for $v$. $\Rightarrow v=0$ or $v=-1$ Check:- $v=0$ $\Rightarrow -2(0)(0+1)=0$ $\Rightarrow 0(1)=0$ $\Rightarrow 0=0$ True. Check:- $v=-1$ $\Rightarrow -2(-1)(-1+1)=0$ $\Rightarrow 2(0)=0$ $\Rightarrow 0=0$ True. Hence, the solutions are $v=0$ and $v=-1$.