$\text{a)}{x}^5-6x^3+9x=0$  

$x\left(x^4-6x^2+9\right)=0$  

$x\left({\left(x^2\right)}^2-2\cdot x^2\cdot 3+3^2\right)=0$  

$x{\left(x^2-3\right)}^2=0$  

$x=0\text{lub}{\left(x^2-3\right)}^2=0$  

$x=0\text{lub}{x}^2-3=0$  

$x=0\text{lub}{x}^2=3$  

$x=0\text{lub}x=\sqrt{3}\text{lub}x=-\sqrt{3}$  

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$\text{b)}{x}^6-7x^2=6x^4$  

$x^6-6x^4-7x^2=0$  

$x^2\left(x^4-6x^2-7\right)=0$  

$x^2\left(x^4+x^2-7x^2-7\right)=0$  

$x^2\left[x^2\left(x^2+1\right)-7\left(x^2+1\right)\right]=0$  

$x^2\left(x^2+1\right)\left(x^2-7\right)=0$  

$x^2=0\text{lub}{x}^2+1=0\text{lub}{x}^2-7=0$  

$x=0\text{lub}\underset{\text{r. sprzeczne}}{x^2=-1}<0\text{lub}{x}^2=7$  

$x=0\text{lub}x=\sqrt{7}\text{lub}x=-\sqrt{7}$