16. For what values of $m$ does the quadratic equation $(5 m-3) x^{2}-$ $4 m x+m+1=0$ have only one root?

Step 1 ：Let's calculate the discriminant and set it equal to 0: \(D = b^2 - 4ac = (-4m)^2 - 4(5m - 3)(m + 1)\)

Step 2 ：Setting the discriminant equal to 0: \(16m^2 - (m + 1)(20m - 12) = 0\)

Step 3 ：Solving for m, we get two values: \(m = -3\) and \(m = 1\)

Step 4 ：\(\boxed{m = -3, m = 1}\)