Expanding the left side of the equation, we have:

(x^2 + 2x + 1)(x^2 + 2x + 4)
= x^2(x^2 + 2x + 4) + 2x(x^2 + 2x + 4) + 1(x^2 + 2x + 4)
= x^4 + 2x^3 + 4x^2 + 2x^3 + 4x^2 + 8x + x^2 + 2x + 4
= x^4 + 4x^3 + 9x^2 + 10x + 4

Setting this equal to 10:

x^4 + 4x^3 + 9x^2 + 10x + 4 = 10

Rearranging the terms:

x^4 + 4x^3 + 9x^2 + 10x + 4 - 10 = 0
x^4 + 4x^3 + 9x^2 + 10x - 6 = 0

This is the final polynomial equation in terms of x.