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Solve.
[tex]\[
(5y - 9)(8 + y) = 0
\][/tex]
(If there is more than one solution, separate them with commas.)
To solve the equation [tex]\((5y - 9)(8 + y) = 0\)[/tex], we can apply 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. So, we will set each factor equal to zero and solve for [tex]\(y\)[/tex] individually.
Let's set each factor to zero and solve:
1. First factor: [tex]\(5y - 9 = 0\)[/tex]
To solve for [tex]\(y\)[/tex], follow these steps:
[tex]\[
5y - 9 = 0
\][/tex]
Add 9 to both sides:
[tex]\[
5y = 9
\][/tex]
Divide both sides by 5:
[tex]\[
y = \frac{9}{5} = 1.8
\][/tex]
2. Second factor: [tex]\(8 + y = 0\)[/tex]
To solve for [tex]\(y\)[/tex], follow these steps:
[tex]\[
8 + y = 0
\][/tex]
Subtract 8 from both sides:
[tex]\[
y = -8
\][/tex]
Therefore, the solutions to the equation [tex]\((5y - 9)(8 + y) = 0\)[/tex] are [tex]\(y = 1.8\)[/tex] and [tex]\(y = -8\)[/tex].
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