Mathematical Induction for Fibonacci sequence[SOLVED]

Ok, this looks different from my other problems with inductions.

Suppose Fn, n is greater or equal to 0 is the Fibonacci sequence (i.e. F0=F1 = 1, and Fn = Fn-1 + Fn-2 for n is greater or equal to 2). Use mathematical induction to prove that

(Fn+2)(Fn)-F^2 * n+1 = (-1)^n for all n greater or equal to 0.

Would I need to change the left side using characteristic equation?

The left side and right side are equal when using the base case = 0. i tried the p(k) and p(k+1) method but looks like I'll need to use a different equation on the left hand side.