Question

What substitution should be used to rewrite 4x^4-21x^2+20=0

Answer 1

You can use z = x², then rewrite the equation as
  4z²-21z+20 = 0
This factors as
  (4z-5)(z-4) = 0
so has solutions
  z = 5/4, 4

The solutions for x are then
  x = ±√z = {-2, -(√5)/2, (√5)/2, 2}