To solve this equation, we first need to expand the expression on the left side of the equation:

(x^-3x-25)^-2(x^+3x-25) = (x^2 - 3x - 25)^-2(x^2 + 3x - 25)

Next, we need to multiply the two expressions:

(x^2 - 3x - 25)(x^2 + 3x - 25) = x^4 + 3x^3 - 25x^2 - 3x^3 - 9x^2 + 75x + 25x^2 + 75x - 625

Combining like terms, we get:

x^4 - 34x^2 + 150x - 625

Now, we need to raise this expression to the power of -2:

(x^4 - 34x^2 + 150x - 625)^-2 = 1 / (x^4 - 34x^2 + 150x - 625)^2

Therefore, the expression on the left side is equal to:

1 / (x^4 - 34x^2 + 150x - 625)^2

Setting this equal to -7, we have:

1 / (x^4 - 34x^2 + 150x - 625)^2 = -7

This equation is now a complex equation that needs to be solved using methods such as factoring, quadratic formula, or completing the square. The final solution will depend on the values of x that satisfy the equation.