To solve this inequality, we will first expand the left side of the inequality:

(х+1)(х-2) = х^2 - 2х + х - 2 = х^2 - х - 2

Therefore, the inequality becomes:

х^2 - х - 2 ≥ х^2 + 3х - 4

Simplifying further:

-x - 2 ≥ 3x - 4

Now, let's isolate x on one side of the inequality by moving terms to the opposite side:

-x - 3x ≥ -4 + 2

-4x ≥ -2

Now, we divide by -4 but remember to flip the sign since we are dividing by a negative number:

x ≤ -2/-4

x ≤ 1/2

So the solution to the inequality (х+1)(х-2) ≥ х² + 3х - 4 is x ≤ 1/2.