## Introductory Algebra for College Students (7th Edition)

The solution set is {0, $\frac{1}{3}$}.
We want to use the zero product property to solve this equation, but we must first make the equation equal to zero. We do this by subtracting $5$ from each side of the equation: $$15x^2 - 5x = 0$$ We see that the two terms can be factored by $5x$ to get: $$5x(3x - 1) = 0$$ We can now use the zero product property to solve the equation. The zero product property states that if a product equals zero, then at least one of the factors must equal zero. We can now take each factor and set each equal to zero: $$5x = 0$$ We divide each side by $5$ to solve for $x$: $$x = 0$$ We now set the second factor equal to zero: $$3x - 1 = 0$$ Add $1$ to each side to set the variable on one side and the constant on the other: $$3x = 1$$ Divide each side by $3$ to solve for $x$: $$x = \frac{1}{3}$$ The solution set is {0, $\frac{1}{3}$}.