1. **State the problem:** Solve the quadratic equation given in factored form: $$y = 10x(6x - 7)$$ for $x$. 2. **Set the equation equal to zero:** To find the roots, set $$y = 0$$: $$0 = 10x(6x - 7)$$ 3. **Use the zero product property:** If a product of factors equals zero, then at least one factor must be zero: $$10x = 0 \quad \text{or} \quad 6x - 7 = 0$$ 4. **Solve each factor for $x$:** - For $$10x = 0$$: $$x = \frac{0}{10} = 0$$ - For $$6x - 7 = 0$$: $$6x = 7$$ $$x = \frac{7}{6}$$ 5. **Final solution:** The solutions are $$x = 0 \quad \text{and} \quad x = \frac{7}{6}$$ 6. **Check the multiple choice answers:** - $\{0, \frac{6}{7}\}$ is incorrect because the second root is $\frac{7}{6}$, not $\frac{6}{7}$. - $\{7, 10\}$ is incorrect. - $\{0, 7\}$ is incorrect. - $\{0, \frac{6}{7}\}$ is repeated and incorrect. Therefore, none of the given options exactly match the correct roots $\{0, \frac{7}{6}\}$. The correct roots are $x=0$ and $x=\frac{7}{6}$.