Question

solve for w .
\\((w^2 + w - 2)(2w - 12) = 0\\)
(if there is more than one solution, separate them with commas.)
\\(w = \\)

Explanation:

Step1: Apply Zero Product Property

Set each factor equal to 0:
$w^2 + w - 2 = 0$, $2w - 12 = 0$

Step2: Solve linear factor first

Isolate $w$ in $2w - 12 = 0$:
$2w = 12 \implies w = \frac{12}{2} = 6$

Step3: Factor quadratic expression

Factor $w^2 + w - 2$:
$(w + 2)(w - 1) = 0$

Step4: Solve quadratic factors

Set each sub-factor to 0:
$w + 2 = 0 \implies w = -2$; $w - 1 = 0 \implies w = 1$

Answer:

$-2, 1, 6$