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[Help Needed] Function to solve polynomial


I am trying to write a function that will help me solve the polynomial f(x)=(x-4)(x+2)(x-1)(x+5)(x-7) (NSolve and Solve functions not preferred)

I can only think of this function:
solution := {Plot[{(x -4)(x + 2)(x - 1)(x + 5)(x - 7)}, {x, -10, 10}, AxesLabel -> TraditionalForm /@ {x, y}]}

Does anyone have better knowledge than me in writing an automated program to solve this polynomial? Say For, While or Do Loop?

Your help will be greatly appreciated.


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