To solve this equation, we will first expand both sides of the equation and simplify:

For the left side of the equation:
(х-1)(х-4)(х+7) = (х^2 - 4х - х + 4)(х+7) = (х^2 - 5х + 4)(х+7) = х^3 + 7х^2 - 5х^2 - 35x + 4x + 28 = х^3 + 2х^2 - 31x + 28

For the right side of the equation:
х(х+1)^2 = х(х^2 + 2x + 1) = х^3 + 2x^2 + x

Now we set the two sides of the equation equal to each other and simplify:

х^3 + 2х^2 - 31x + 28 = х^3 + 2x^2 + x
Rearranging terms:
2х^2 - 31x + 28 = 2x^2 + x

Solving for x, we get:
-31x + 28 = x
Combining like terms:
-31x - x = -28
-32x = -28
x = -28 / -32
x = 7/8

Therefore, the solution to the equation is x = 7/8.