Solve the system of equations

y=-2(x^2-1)
y=2(x^4-2x^2 +1)

The second equation is

y = 2(x^2-1)^2
so,
-2(x^2-1) = 2(x^2-1)^2
so, x^2-1=0 is a solution, meaning x = ±1
Otherwise, divide by 2(x^2-1) to get

-1 = (x^2-1)
x = 0

So, the solutions are -1,0,1

View the graphs at

http://www.wolframalpha.com/input/?i=solve+y%3D-2%28x^2-1%29%2C+y%3D2%28x^4-2x^2+%2B1%29