Question

solve for w.
(3w - 21)(w^2 + 10w + 24) = 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:
$3w - 21 = 0$, $w^2 + 10w + 24 = 0$

Step2: Solve linear equation

Isolate $w$ in $3w - 21 = 0$:
$3w = 21$
$w = \frac{21}{3} = 7$

Step3: Factor quadratic equation

Factor $w^2 + 10w + 24$:
$(w + 4)(w + 6) = 0$

Step4: Solve factored quadratic

Set each sub-factor to 0:
$w + 4 = 0 \implies w = -4$
$w + 6 = 0 \implies w = -6$

Answer:

$w = -6, -4, 7$