1. The problem is to find the two solutions to the equation $$(5x - 1)(x - 2) = 0$$. 2. According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero. So, we set each factor equal to zero: $$5x - 1 = 0$$ $$x - 2 = 0$$ 3. Solve each equation separately. For $$5x - 1 = 0$$: Add 1 to both sides: $$5x - 1 + 1 = 0 + 1$$ $$5x = 1$$ Divide both sides by 5: $$\cancel{5}x = \frac{1}{\cancel{5}}$$ $$x = \frac{1}{5}$$ 4. For $$x - 2 = 0$$: Add 2 to both sides: $$x - 2 + 2 = 0 + 2$$ $$x = 2$$ 5. Therefore, the two solutions to the equation are: $$x = \frac{1}{5} \quad \text{and} \quad x = 2$$