To solve the equation (х^2 + х + 4)^2 + 8х(х^2 + х + 4) +15х^2 = 0, let's expand it step by step:

First, expand (х^2 + х + 4)^2:

(х^2 + х + 4)^2 = (х^2 + х + 4)(х^2 + х + 4)
= (х^2)(х^2) + (х^2)(х) + (х^2)(4) + (х)(х^2) + (х)(х) + (х)(4) + (4)(х^2) + (4)(х) + (4)(4)
= х^4 + х^3 + 4х^2 + х^3 + х^2 + 4х + 4х^2 + 4x + 16
= х^4 + 2х^3 + 9х^2 + 8х + 16

Next, expand 8х(х^2 + х + 4):

8х(х^2 + х + 4) = 8х(х^2) + 8х(х) + 8х(4)
= 8х^3 + 8х^2 + 32х

Now, substitute the expansions back into the equation:

(х^4 + 2х^3 + 9х^2 + 8х + 16) + (8х^3 + 8х^2 + 32х) + 15x^2 = 0
х^4 + 2х^3 + 9х^2 + 8х + 16 + 8х^3 + 8х^2 + 32х + 15x^2 = 0
х^4 + 2х^3 + 8х^3 + 9х^2 + 8х^2 + 15x^2 + 8х + 32х + 16 = 0
х^4 + 10х^3 + 32х^2 + 40x + 16 = 0

So, the simplified form of the given equation is х^4 + 10х^3 + 32х^2 + 40x + 16 = 0.