To find the solutions to the equation [tex]\((x-9)(x+5) = 0\)[/tex], we need to solve for [tex]\(x\)[/tex] by setting each factor equal to zero. This method is based on the Zero Product Property, which states that if the product of two factors is zero, at least one of the factors must be zero.
1. Set the first factor equal to zero:
[tex]\[
x - 9 = 0
\][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[
x = 9
\][/tex]
So, one solution is [tex]\(x = 9\)[/tex].
2. Set the second factor equal to zero:
[tex]\[
x + 5 = 0
\][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[
x = -5
\][/tex]
So, another solution is [tex]\(x = -5\)[/tex].
Thus, the two solutions to the equation [tex]\((x-9)(x+5) = 0\)[/tex] are [tex]\(\boxed{9 \text{ and } -5}\)[/tex].
