To solve the equation \( v^2 + 25v = 0 \), we can factor out the common term:
\[ v(v + 25) = 0 \]
Setting each factor equal to zero gives us:
- \( v = 0 \)
- \( v + 25 = 0 \Rightarrow v = -25 \)
Thus, the solutions are:
\[ v = 0 \quad \text{and} \quad v = -25 \]