(6x+1)^2(1-x)+(5-6x)^2(x+1)=14

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Expanding both terms, we get:

(6x+1)^2(1-x) = (36x^2 + 12x + 1)(1-x)
= 36x^2 + 12x - 36x^3 - 12x^2 + 1 - x

(5-6x)^2(x+1) = (25 - 60x + 36x^2)(x+1)
= 25x + 25 - 60x^2 - 60x + 36x^2 + 36x
= -24x^2 - 35x + 25

Adding these two expressions together, we get:

36x^2 + 12x - 36x^3 - 12x^2 + 1 - x - 24x^2 - 35x + 25 = 14

Combining like terms:

-36x^3 + 0x^2 - 35x - 46 = 14

Rearranging terms:

-36x^3 - 35x - 60 = 0

Therefore, the equation simplifies to:

36x^3 + 35x + 60 = 0.