To solve this inequality, we need to determine the values of x that satisfy the inequality.
First, we can find the critical values of x by setting each factor equal to zero and solving for x:
(x-3)^2 = 0 => x = 3 (double root)
2x+5 = 0 => x = -5/2
x-1 = 0 => x = 1
These critical values divide the number line into four intervals: (-infinity, -5/2), (-5/2, 1), (1, 3), and (3, infinity).
We can now test each interval to see if it satisfies the inequality. We can use a sign chart or test points within each interval to do this.
For example, in the interval (-infinity, -5/2), we can choose a test point such as x=-3 and evaluate the expression:
(x-3)^2(2x+5)(x-1) = (-6)^2(-1)(-4) = 144
Since this expression is positive, we know that this interval does not satisfy the inequality.
Using similar reasoning, we can test the other intervals and find that the solutions to the inequality are:
x <= -5/2 or 1 <= x <= 3
Therefore, the solution to the inequality is:
x ∈ (-infinity, -5/2] U [1, 3]