Let's simplify the given equation:

(x^2 + 2x)^2 - 14(x^2 + 2x) - 15 = 0

Expanding the square of (x^2 + 2x):

(x^2 + 2x)(x^2 + 2x) - 14(x^2 + 2x) - 15 = 0
(x^4 + 2x^3 + 2x^3 + 4x^2) - 14x^2 - 28x - 15 = 0
x^4 + 4x^3 + 4x^2 - 14x^2 - 28x - 15 = 0
x^4 + 4x^3 - 10x^2 - 28x - 15 = 0

Now we have a quartic equation that we can solve using various methods like factoring, grouping, or using the quadratic formula.