Х^4+5х^3+4х^2-24х-24=0

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To solve this polynomial equation, we can factor it by grouping:

х^4 + 5х^3 + 4х^2 - 24х - 24 = 0
х^3(х + 5) + 4(х^2 - 6) = 0
х^3(х + 5) + 4(х^2 - 6) = 0
х^3(х + 5) + 4(х^2 - 6) = 0
х^3(х + 5) + 4(х - 6)(x + 1) = 0
(х^3 + 4)(х + 5) - 4(х + 6) = 0
(х^3 + 4)(х + 5) - 4(х + 6) = 0

Therefore, the solutions to the equation are x = 1, x = -2, x = -3, x = -4.