Solve Quadratic 63E454

1. **State the problem:** We need to find the values of $x$ that satisfy the equation $$(3x - 1)(x - 5) = 0$$. 2. **Recall the zero product property:** If the product of two factors is zero, then at least one of the factors must be zero. That is, if $$A \cdot B = 0$$, then either $$A = 0$$ or $$B = 0$$. 3. **Apply the zero product property:** Set each factor equal to zero: $$3x - 1 = 0$$ $$x - 5 = 0$$ 4. **Solve each equation:** For $$3x - 1 = 0$$: Add 1 to both sides: $$3x - 1 + 1 = 0 + 1$$ $$3x = 1$$ Divide both sides by 3: $$\frac{\cancel{3}x}{\cancel{3}} = \frac{1}{3}$$ $$x = \frac{1}{3}$$ For $$x - 5 = 0$$: Add 5 to both sides: $$x - 5 + 5 = 0 + 5$$ $$x = 5$$ 5. **Final answer:** The two solutions to the equation are $$x = \frac{1}{3}$$ and $$x = 5$$.