To solve this equation, let's first make a substitution. Let (u = x^2 + 4).

Now, our equation becomes:

(u^2 - 7u + 10 = 0)

This is a quadratic equation that we can factor or solve using the quadratic formula.

Factoring the equation, we get:

((u - 2)(u - 5) = 0)

This yields two solutions:

(u = 2) or (u = 5)

Now, substitute back with (u = x^2 + 4):

For (u = 2):

(x^2 + 4 = 2)

(x^2 = -2)

This equation has no real solutions, as you cannot take the square root of a negative number.

For (u = 5):

(x^2 + 4 = 5)

(x^2 = 1)

(x = ±1)

Therefore, the solutions to the equation ((x^2+4)^2-7(X^2+4)+10=0) are (x = 1) and (x = -1).