Alright, let's solve the equation [tex]\((4w - 6)(8 - w) = 0\)[/tex] step-by-step.
First, we need to understand that for the product of two factors to be zero, at least one of the factors must be zero. So, we need to solve each factor set equal to zero:
1. Solve for [tex]\(w\)[/tex] in the first factor:
[tex]\[
4w - 6 = 0
\][/tex]
Add 6 to both sides:
[tex]\[
4w = 6
\][/tex]
Divide both sides by 4:
[tex]\[
w = \frac{6}{4} = \frac{3}{2}
\][/tex]
2. Solve for [tex]\(w\)[/tex] in the second factor:
[tex]\[
8 - w = 0
\][/tex]
Add [tex]\(w\)[/tex] to both sides:
[tex]\[
8 = w
\][/tex]
Therefore, the solutions to the equation [tex]\((4w - 6)(8 - w) = 0\)[/tex] are:
[tex]\[
w = \frac{3}{2}, 8
\][/tex]
So, the answers are:
[tex]\[
w = \boxed{\frac{3}{2}}, \boxed{8}
\][/tex]
