To solve the equation [tex]\((3x + 2)(x - 5) = 0\)[/tex], we can use the zero product property. This property states that if the product of two factors is zero, then at least one of the factors must be zero. That is, we set each factor equal to zero and solve for [tex]\(x\)[/tex].
1. Set the first factor equal to zero:
[tex]\[
3x + 2 = 0
\][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[
3x = -2 \\
x = \frac{-2}{3}
\][/tex]
2. Set the second factor equal to zero:
[tex]\[
x - 5 = 0
\][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[
x = 5
\][/tex]
So, we have two solutions: [tex]\(x = \frac{-2}{3}\)[/tex] and [tex]\(x = 5\)[/tex].
Now, we need to determine which solution has the highest value. Comparing [tex]\(\frac{-2}{3}\)[/tex] and [tex]\(5\)[/tex], it is clear that [tex]\(5\)[/tex] is the larger value.
Thus, the solution with the highest value is:
[tex]\[
\boxed{5}
\][/tex]
