Solve using polynomial equations by factoring and using the principle of zero product.

X^3 - 27 = 0

Here x^3-27=0 can be written as

x^3=27 and it also can be,

x^3=3^3

then on comparing both we got,

x=3 ...

Hope it will satisfy you

(x-3) (x^2+3x+27) = 0

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Solve the quadratic factor:

x^2 + 3x + 27 = 0

x = [-3 + - sqrt (9-4*27) / 2

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x = [-3 + - sqrt (-99) ]/2

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x = [-3+-3sqrt (11) i]/2 (2 complex number solutions)

x = 3 (the Real Number solution)