(x-1)³+(x-2)³+(x-3)³+(x-4)³+(x-5)³=0
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Before going to solve, let's know some important formula regarding the same.
if a + b + c = 0 then a³ + b³ + c³ - 3abc = 0
here given, (3x + 1)³ + (x - 3)³ + (4 - 2x) + 6(3x + 1)(x - 3)(x - 2) = 0
⇒(3x + 1)³ + (x - 3)³ + {2(x - 2)}³ -3(3x + 1)(x - 3){-2(x - 2)} = 0
we see it follows a³ + b³ + c³ - 3abc = 0
then must be a + b + c = 0
⇒(3x + 1) + (x - 3) + {-2(x - 2)} = 0
⇒3x + 1 + x - 3 + 4 - 2x = 0
⇒2x + 2 = 0
⇒x = -1
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