$A-(x+3)^{2}=-4 x-15$

Step 1 ：Expand the equation: \(A - (x + 3)^2 = -4x - 15 \Rightarrow A - x^2 - 6x - 9 = -4x - 15\)

Step 2 ：Isolate x: \(x^2 + 2x - (A + 6) = 0\)

Step 3 ：Final Answer: \(\boxed{x = -\sqrt{A + 7} - 1} \) and \(\boxed{x = \sqrt{A + 7} - 1}\)