Question

solve for w.
(w² + 3w - 10)(4w + 20) = 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:
$w^2 + 3w - 10 = 0$, $4w + 20 = 0$

Step2: Solve linear equation first

Isolate $w$ in $4w + 20 = 0$:
$4w = -20$
$w = \frac{-20}{4} = -5$

Step3: Factor quadratic equation

Factor $w^2 + 3w - 10$:
$(w+5)(w-2) = 0$

Step4: Solve factored quadratic

Set each sub-factor to 0:
$w+5=0 \implies w=-5$; $w-2=0 \implies w=2$

Step5: Collect unique solutions

Remove duplicate solution.

Answer:

$-5, 2$