Answer:
x ∈ {-0.924, 1.400, 1.624}
Step-by-step explanation:
The local extrema of the function are nicely shown by a graphing calculator.
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If you like you can find the zeros of the derivative.
... f'(x) = 100x³ -210x² -52x +210
By graphing or other means, you can determine that this has a zero at x=1.4, so can be factored as ...
... f'(x) = 2(5x -7)(10x² -7x -15)
The quadratic factor has roots at x = 0.35 ± √1.6225 ≈ {-0.924, 1.624}
