Question

(x-1)(x-2)(x-3)(x-4)=120

Answer 1

$(x - 1)(x - 2)(x - 3)(x - 4) = 120 \\ (x - 1)(x - 4)(x - 2)(x - 3) = 0 \\ ( {x}^{2} - 4x - x + 5)( {x}^{2} - 3x - 2x + 5) = 0 \\ {x}^{2} - 5x + 4)( {x}^{2} - 5x + 6) = 0 \\ let \: {x}^{2} - 5x = y \\ (y + 4)(y + 6) = 0 \\ {y}^{2} + 6y + 4y + 24 = 0 \\ y(y + 6) + 4(y + 6) = 0 \\ (y + 6)(y + 4) = 0 \\ ify + 6 = 0 \\ {x}^{2} - 5x + 6 = 0 \\ {x}^{2} - 3x - 2x + 6 = 0 \\ x(x - 3) - 2(x - 3) = 0 \\ (x - 3)(x - 2) = 0 \\ if \: x - 3 = 0 \\ x = 3 \\ x - 2 = 0 \\ x = 2 \\ if \: y + 4 = 0 \\ {x}^{2} - 5x + 4 = 0 \\ {x}^{2} - 4x - x + 4 = 0 \\ x(x - 4) - 1(x - 4) = 0 \\ (x - 4)(x - 1) = 0 \\ if \: x - 4 = 0 \\ x = 4 \\ if \: x - 1 = 0 \\ x = 1$
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