Step-by-step EXPLANATION:

(x−1)(x−2)(x−3)(x−4)=120(x−1)(x−4)(x−2)(x−3)=0(x2−4x−x+5)(x2−3x−2x+5)=0x2−5x+4)(x2−5x+6)=0letx2−5x=y(y+4)(y+6)=0y2+6y+4y+24=0y(y+6)+4(y+6)=0(y+6)(y+4)=0ify+6=0x2−5x+6=0x2−3x−2x+6=0x(x−3)−2(x−3)=0(x−3)(x−2)=0ifx−3=0x=3x−2=0x=2ify+4=0x2−5x+4=0x2−4x−x+4=0x(x−4)−1(x−4)=0(x−4)(x−1)=0ifx−4=0x=4ifx−1=0x=1\begin{lgathered}(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\end{lgathered}

(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

letx

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

ifx−3=0

x=3

x−2=0

x=2

ify+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

ifx−4=0

x=4

ifx−1=0

x=1

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