How To Factor 4x2 -32x + 80?

It does not factor nicely. To determine this,
1. Factor out 4
  4(x^2 - 8x + 20)
2. Look for factors of 20 that add to 8.
  20 = 1*20 = 2*10 = 4*5
  These pairs of factors add to 21, 12, and 9, respectively. There are no integer factors that add to 8, so we know this will not factor nicely.
3. Determine what the roots are using the quadratic formula.
  X = (-(-8) ±√((-8)^2 - 4(1)(20)))/(2*1)
  = (8 ±√(64-80))/2
  = (8 ±√-16)/2
  = 4 ± √-4    (unless you are studying complex numbers, you must say this solution doesn't exist)
  = 4 ± 2i    (this is a complex conjugate pair. √-1 = i)
4. Given what we learned above, the factorization of your expression is
  4(x - 4 - 2i)(x - 4 + 2i)