Show that the tangent to the curve y=(x^2+x-2)^3 +3 at the point (1,3) is also tangent to the curve at another point.

Just a question about how I get the answer to this question.. is this method correct?

I find the derivative of y. Then find the equation of the tangent at x=1. Make the equation of the tangent at x=1 equal to the original function. Solve for x.