How can I modify 0=x^4(x-43)+40x^2(18x-145)+16(1375x-1884) further?

hi Gibsonj338,

$$0=x^4(x-43)+40x^2(18x-145)+16(1375x-1884)$$

I do not know any way to do this without expanding first and then looking for factors

in this case (x-12) is a factor.

12 is the only real solution.  There are 2 irrational solutions and 2 complex solutions

http://www.wolframalpha.com/input/?i=0%3Dx%5E4%28x-43%29%2B40x%5E2%2818x-145%29%2B16%281375x-1884%29+#