Question

solve for v .
(3v + 6)(v² - 9v + 20) = 0
(if there is more than one solution, separate them with commas.)
v =

Explanation:

Step1: Apply Zero-Product Property

If \(ab = 0\), then \(a = 0\) or \(b = 0\). So, set \(3v + 6 = 0\) and \(v^2 - 9v + 20 = 0\) separately.

Step2: Solve \(3v + 6 = 0\)

Subtract 6 from both sides: \(3v = -6\). Divide by 3: \(v = -2\).

Step3: Solve \(v^2 - 9v + 20 = 0\)

Factor the quadratic: \(v^2 - 9v + 20 = (v - 4)(v - 5) = 0\). Set each factor to 0: \(v - 4 = 0\) gives \(v = 4\); \(v - 5 = 0\) gives \(v = 5\).

Answer:

\(v = -2, 4, 5\)