Certainly! Let's solve the equation \(6v^2 = -24v\) step-by-step.
1. Initial Equation:
[tex]\[
6v^2 = -24v
\][/tex]
2. Rearrange the Equation: Move all terms to one side of the equation to set it equal to 0:
[tex]\[
6v^2 + 24v = 0
\][/tex]
3. Factoring: Notice that both terms on the left side have a common factor of \(6v\). Factor out \(6v\):
[tex]\[
6v(v + 4) = 0
\][/tex]
4. Using the Zero-Product Property: The zero-product property states that if a product of two factors is zero, then at least one of the factors must be zero. So, set each factor equal to zero and solve for \(v\):
[tex]\[
6v = 0 \quad \text{or} \quad v + 4 = 0
\][/tex]
5. Solve Each Equation:
[tex]\[
6v = 0 \implies v = 0
\][/tex]
[tex]\[
v + 4 = 0 \implies v = -4
\][/tex]
Thus, the solutions to the equation \(6v^2 = -24v\) are \(v = 0\) and \(v = -4\).
So, the values of \(v\) are:
[tex]\[
v = 0 \quad \text{ and } \quad v = -4
\][/tex]
