Question

solve for v.
\\((v^2 - 2v - 15)(6v - 30) = 0\\)
(if there is more than one solution, separate them with commas.)
\\(v = \square\\)

Explanation:

Step1: Apply Zero Product Property

If \( (a)(b) = 0 \), then either \( a = 0 \) or \( b = 0 \). So we set each factor equal to zero:

1. \( v^2 - 2v - 15 = 0 \)
2. \( 6v - 30 = 0 \)

Step2: Solve \( 6v - 30 = 0 \)

Add 30 to both sides: \( 6v = 30 \)
Divide by 6: \( v = \frac{30}{6} = 5 \)

Step3: Solve \( v^2 - 2v - 15 = 0 \)

Factor the quadratic: We need two numbers that multiply to -15 and add to -2. Those numbers are -5 and 3.
So, \( v^2 - 2v - 15 = (v - 5)(v + 3) = 0 \)
Set each factor to zero:

• \( v - 5 = 0 \) gives \( v = 5 \)
• \( v + 3 = 0 \) gives \( v = -3 \)

Answer:

-3, 5