Let's simplify the given equation step by step:

(X-5)™ + 2x(x-3) = (x™-10x+25)

Expanding the terms on the left side:
(X-5)(X-5) + 2x(x-3) = (x™-10x+25)
(X^2 - 5X - 5X + 25) + 2x^2 - 6x = (x™-10x+25)
(X^2 - 10X + 25) + 2x^2 - 6x = x^2 - 10x + 25

Now simplify the terms and combine like terms:
X^2 - 10X + 25 + 2x^2 - 6x = x^2 - 10x + 25
3x^2 - 16x + 25 = x^2 - 10x + 25

Combine the x^2 terms on both sides:
3x^2 - x^2 - 16x + 10x + 25 = 25

Simplify:
2x^2 - 6x = 0

Factor:
2x(x - 3) = 0

Set each factor to zero:
2x = 0 or x - 3 = 0

Solve for x:
x = 0 or x = 3

Therefore, the solutions to the original equation are x = 0 and x = 3.