a)

$6x\left(x+7\right)\left(x-9\right)=0$

$$\begin{gathered} 6x=0\text{lub}x+7=0\text{lub}x-9=0 \\ x=0\text{lub}x=-7\text{lub}x=9 \end{gathered}$$

$x\in \left\{-7,0,9\right\}$

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b)

$\frac{1}{4}x\left(2x-1\right)\left(5x+2\right)=0$

$$\begin{gathered} \frac{1}{4}x=0\text{lub}2x-1=0\text{lub}5x+2=0 \\ x=0\text{lub}x=\frac{1}{2}\text{lub}x=-\frac{2}{5} \end{gathered}$$

$x\in \left\{-\frac{2}{5},0,\frac{1}{2}\right\}$

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c)

$\left(x-2\right)\left(x+3\right)\left(4x+1\right)=0$

$$\begin{gathered} x-2=0\text{lub}x+3=0\text{lub}4x+1=0 \\ x=2\text{lub}x=-3\text{lub}x=-\frac{1}{4} \end{gathered}$$

$x\in \left\{-3,-\frac{1}{4},2\right\}$

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d)

$\left(x+5\right)\left(x-4\right)\left(2x-4\right)=0$

$$\begin{gathered} x+5=0\text{lub}x-4=0\text{lub}2x-4=0 \\ x=-5\text{lub}x=4\text{lub}x=2 \end{gathered}$$

$x\in \left\{-5,2,4\right\}$