Question

solve for w .
\\((w^2 + 5w - 6)(2w + 18) = 0\\)
(if there is more than one solution, separate them with commas.)
\\(w = \square\\)

Explanation:

Step1: Apply zero - product property

If \(ab = 0\), then either \(a = 0\) or \(b = 0\). For the equation \((w^{2}+5w - 6)(2w + 18)=0\), we set each factor equal to zero:

• Set \(w^{2}+5w - 6=0\) and \(2w + 18 = 0\).

Step2: Solve \(2w+18 = 0\)

Subtract 18 from both sides: \(2w=-18\).
Divide both sides by 2: \(w=\frac{-18}{2}=-9\).

Step3: Solve \(w^{2}+5w - 6 = 0\)

Factor the quadratic equation. We need two numbers that multiply to \(-6\) and add up to 5. The numbers are 6 and - 1.
So, \(w^{2}+5w - 6=(w + 6)(w - 1)=0\).
Set each factor equal to zero:

• If \(w + 6=0\), then \(w=-6\).
• If \(w - 1=0\), then \(w = 1\).

Answer:

\(w=-9,-6,1\)