Expanding the left side of the equation:
(x^2 + 2x)(x^2 + 2x - 2) = x^2(x^2 + 2x - 2) + 2x(x^2 + 2x - 2)= x^4 + 2x^3 - 2x^2 + 2x^3 + 4x^2 - 4x= x^4 + 4x^3 + 2x^2 - 4x
Therefore, the equation becomes:
x^4 + 4x^3 + 2x^2 - 4x = 3
Now, we can simplify this equation by moving all terms to one side:
x^4 + 4x^3 + 2x^2 - 4x - 3 = 0
This is a quartic equation that can be solved by various methods, such as factoring, using the rational root theorem, or using numerical methods.
Expanding the left side of the equation:
(x^2 + 2x)(x^2 + 2x - 2) = x^2(x^2 + 2x - 2) + 2x(x^2 + 2x - 2)
= x^4 + 2x^3 - 2x^2 + 2x^3 + 4x^2 - 4x
= x^4 + 4x^3 + 2x^2 - 4x
Therefore, the equation becomes:
x^4 + 4x^3 + 2x^2 - 4x = 3
Now, we can simplify this equation by moving all terms to one side:
x^4 + 4x^3 + 2x^2 - 4x - 3 = 0
This is a quartic equation that can be solved by various methods, such as factoring, using the rational root theorem, or using numerical methods.