Chapter 4.4, Problem 13E

Find the solutions of the congruence $\text{15}{x}^{\text{2}}\text{+19}x=\text{5}\left(\text{mod 11}\right)$ . [Hint: Show the congruence is equivalent to the congruence $\text{15}{x}^{\text{2}}\text{+19}x+\text{6}\equiv 0\left(\text{mod 11}\right)$ .

Factor the left-hand side of the congruence; show that a solution of the quadratic congruence is a solution of one of the two different linear congruences.]