(x+2)^2*(x-5)^3=(x-5)*(x+2)^4

(x + 2)^2*(x - 5)^3 - (x + 2)^4*(x - 5) =0
(x - 5)(x+ 2)^2( (x - 5)^2 - (x + 2)^2) = 0
( x - 5)(x +2)^2 *( x^2-10x+25 - (x^2+4x + 4))= 0
(x- 5)(x+ 2)^2*( x^2-10x+25-x^2-4x-4) =0
(x - 5)(x + 2)^2*(21 - 14x) = 0
(x- 5)(x + 2)(x + 2)(21 - 14x) =0
Произведение равно 0,когда один из множителей равен 0,значит,
x - 5 = 0
x = 5
x + 2 =0
x = - 2
21 - 14x = 0
- 14x = - 21
14x =21
x = 1,5
Ответ: x1 = 5, x2 = - 2, x3 = 1,5.