Certainly! Let's solve the equation [tex]\((5x + 4)(5x - 4) = 0\)[/tex].
### Step-by-Step Solution:
1. Recognize the Zero Product Property: The zero product property states that if the product of two factors is zero, at least one of the factors must be zero. So, we set each factor to zero and solve for [tex]\(x\)[/tex] independently.
[tex]\[(5x + 4) = 0 \quad \text{or} \quad (5x - 4) = 0\][/tex]
2. Solve the First Equation:
[tex]\[
5x + 4 = 0
\][/tex]
To isolate [tex]\(x\)[/tex], subtract 4 from both sides:
[tex]\[
5x = -4
\][/tex]
Now, divide both sides by 5:
[tex]\[
x = -\frac{4}{5}
\][/tex]
3. Solve the Second Equation:
[tex]\[
5x - 4 = 0
\][/tex]
To isolate [tex]\(x\)[/tex], add 4 to both sides:
[tex]\[
5x = 4
\][/tex]
Now, divide both sides by 5:
[tex]\[
x = \frac{4}{5}
\][/tex]
4. Combine the Solutions: The solutions to the equation [tex]\((5x + 4)(5x - 4) = 0\)[/tex] are:
[tex]\[
x = -\frac{4}{5} \quad \text{and} \quad x = \frac{4}{5}
\][/tex]
### Conclusion:
The values of [tex]\(x\)[/tex] that satisfy the given equation are:
[tex]\[
x = -\frac{4}{5} \quad \text{and} \quad x = \frac{4}{5}
\][/tex]
