(х+2)^4 + 2х^2+8х-16=0

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To solve this equation, we start by expanding the expression (х+2)^4 using the binomial theorem:

(х+2)^4 = x^4 + 4x^3(2) + 6x^2(2)^2 + 4x(2)^3 + 2^4
= x^4 + 8x^3 + 24x^2 + 32x + 16

Now substitute this expansion back into the original equation:

x^4 + 8x^3 + 24x^2 + 32x + 16 + 2x^2 + 8x - 16 = 0

Combine like terms:

x^4 + 8x^3 + 26x^2 + 40x = 0

Now we have a quartic equation that we can factor or solve using numerical methods to find the solutions for x.