The polynomial \(p(x)=(2x-1)(x+k)-12\), where \(k\) is a constant.

(i) Write down the value of \(p(-k)\).

When \(p(x)\) is divided by \(x+3\), the remainder is \(23\).

(ii) Find the value of \(k\).

(iii) Using your value of \(k\), show that the equation \(p(x)=-25\) has no real solutions.