#### Answer

{-5, -1/3, 5}

#### Work Step by Step

1. Make sure all factors are fully factored.
$x^{2}$ - 25 = (x + 5)(x - 5)
2. Apply the zero factor property.
a) x + 5 = 0
b) x - 5 = 0
c) 3x + 1 = 0
3. Solve each linear equation.
a) x = -5
b) x = 5
c) x = -1/3
The solutions are {-5, -1/3, 5}.