Answer
The solution set is {0, $\frac{1}{3}$}.
Work Step by Step
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, $\frac{1}{3}$}.
