To solve the equation [tex]\((8b + 5)(3b - 9) = 0\)[/tex], we need to use the Zero Product Property which states that if the product of two factors is zero, then at least one of the factors must be zero. This gives us two separate equations to solve for [tex]\( b \)[/tex]:
1) [tex]\( 8b + 5 = 0 \)[/tex]
2) [tex]\( 3b - 9 = 0 \)[/tex]
Let's solve these equations one by one:
1) Solve [tex]\( 8b + 5 = 0 \)[/tex]:
[tex]\[
8b + 5 = 0
\][/tex]
Subtract 5 from both sides:
[tex]\[
8b = -5
\][/tex]
Divide both sides by 8:
[tex]\[
b = -\frac{5}{8}
\][/tex]
2) Solve [tex]\( 3b - 9 = 0 \)[/tex]:
[tex]\[
3b - 9 = 0
\][/tex]
Add 9 to both sides:
[tex]\[
3b = 9
\][/tex]
Divide both sides by 3:
[tex]\[
b = 3
\][/tex]
Therefore, the solutions to the equation [tex]\((8b + 5)(3b - 9) = 0\)[/tex] are:
[tex]\[
b = -\frac{5}{8}, 3
\][/tex]
These are the values of [tex]\( b \)[/tex] that satisfy the given equation.
