Solve the inequality and write your answer in interval notation

(x-2)(x+4)(x-5)^2<0

The answer will come from one - or more - of these intervals  (-∞, -4), (-4, 2), (2,∞)

Notice that any x values on   (-∞, -4). (2, ∞)  make the equality false

And any x values on (-4, 2)  make it true

Here's a graph........https://www.desmos.com/calculator/xy1kcpagbt

The inequality holds when -4 < x < 2

Look at the graph below and think carefully about what happens in each region:

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