(3x-7)^2(x+5) = (3x-7)(x+5)^2
Expanding both sides:

(9x^2 - 42x + 49)(x + 5) = (3x - 7)(x^2 + 10x + 25)

Expanding further:

9x^3 + 45x^2 - 42x^2 - 210x + 49x + 245 = 3x^3 + 30x^2 - 7x^2 - 70x + 3x - 35

Combining like terms:

9x^3 + 3x^3 + 45x^2 - 42x^2 - 7x^2 + 49x - 70x + 3x + 245 + 35 = 0

12x^3 - 6x^2 - 18x + 280 = 0

Dividing through by 2 to simplify:

6x^3 - 3x^2 - 9x + 140 = 0

This cubic equation does not have a nice simple solution. However, you can use numerical methods to find an approximate solution.