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Answer:
Solve this problem by factoring, we need to consider the equation:
[tex](3n - 2)(4n + 1) = 0[/tex]
Use the zero-product property, which states that if the product of two factors is zero, at least one of the factors must be zero. Therefore:
[tex]3n - 2 = 0 \quad \text{or} \quad 4n + 1 = 0[/tex]
[tex]3n - 2 + 2 = 0 + 2 \implies 3n = 2[/tex]
[tex]n = \frac{2}{3}[/tex]
[tex]{4n + 1 - 1 = 0 - 1 \implies 4n = -1}[/tex]
[tex]n = -\frac{1}{4}[/tex]
The solutions to the equation (3n - 2)(4n + 1) = 0) are:
[tex]n = \frac{2}{3} \quad \text{or} \quad n = -\frac{1}{4}[/tex]