Let \(x\) be a value such that \(9x^2 - 18x - 16 = 0\) and \(15x^2 + 28x + 12 = 0.\) What is the value of \(x\)? Express your answer as a simplified common fraction.

Since they both are equal to 0, we can set them equal to each other.

Therefore, \(9x^2-18x-16=15x^2+28x+12\), and by solving the quadratic, we get two solutions, \(x=-7,\:x=-\frac{2}{3}\), but by guess and check, \(\boxed{x=-\frac{2}{3}}.\)