Final answer:
To solve the equation v(3v + 1) = 0, set each factor equal to zero and solve for v. The solutions are v = 0 and v = -1/3.
Step-by-step explanation:
To solve the equation v(3v + 1) = 0, we can use the zero product property. According to this property, if a product of factors is equal to zero, then at least one of the factors must be zero. So, we set each factor equal to zero and solve for v:
1) v = 0
2) 3v + 1 = 0
Solving the second equation, we subtract 1 from both sides and divide by 3 to obtain v = -1/3. Therefore, the solutions to the equation are v = 0 and v = -1/3.