Tangent Line to y = x^4 - 2x^2 - x shared by two points

[k3232x]

I'm having difficulty with the following exercise:

Find the two points on the curve y = x^4 - 2x^2 - x that have a common tangent line.

 

[k3232x]

I took the derivative of the equation and got:

y`= 4x^3 - 4x - 1 and put that into the equation of a tangent to the curve:

y=(4x^3 - 4x - 1)x + c

Then replaced y with the original equation:

x^4 - 2x^2 - x = (4x^3 -4x - 1)x + c

Then solved for the intercept:

c= -3x^4 + 2x^2

Need 2 points which have a common tangent, (a,b) and (c,d) then:

4a^3 -4a -1 = 4c^3 -4c -1 and

-3a^4 + 2a^2 = -3c^4 - 2c^2

Now here's where I am stuck. I don't know how to solve these equations which would then give me the points (a,b) and (c,d) that i need for a common tangent line.

 

[k3232x]

Any ideas? or am i doing something wrong? Anything would be very helpful