Expand and move every term to one side.
\(\begin{array}{rcl} (2x + 5)(x - 3) &=& 14 + 7x -8\\ 2x^2 + 5x - 6x - 15 &=& 14 + 7x - 8\\ 2x^2 -8x-7&=&0 \end{array}\)
Let a and b be the possible values of x. Then by Vieta's formulae, \(a + b = 4\).
Therefore, the sum of possible values of x is 4.