$\text{a)}6x^4+2x^3=0\mid :6$

$x^4+\frac{1}{3}{x}^3=0$

$x^3\left(x+\frac{1}{3}\right)=0$

$x^3=0\text{lub}x+\frac{1}{3}=0$

$x=0\text{lub}x=-\frac{1}{3}$

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$b)-x^5+4x^3=0|\cdot \left(-1\right)$

$x^5-4x^3=0$

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

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

$x^3=0\text{lub}x-2=0\text{lub}x+2=0$

$x=0\text{lub}x=2\text{lub}x=-2$

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$\text{c)}{x}^6+x=x+2x^4$

$x^6-2x^4=0$

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

$x^4=0\text{lub}{x}^2-2=0$

$x=0\text{lub}{x}^2=2$  

$x=0\text{lub}x=\sqrt{2}\text{lub}x=-\sqrt{2}$

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$\text{d)}\frac{x^4-4x^3}{2}=\frac{x^5-6x^3}{3}\mid \cdot 6$

$3x^4-12x^3=2x^5-12x^3$

$3x^4-2x^5=0$

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

$x^4=0\text{lub}3-2x=0$

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

$x=0\text{lub}x=\frac{3}{2}$  

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$\text{e)}\frac{1}{6}{x}^3+2x^2+6x=0\mid \cdot 6$

$x^3+12x^2+36x=0$

$x\left(x^2+12x+36\right)=0$

$x{\left(x+6\right)}^2=0$

$x=0\text{lub}x+6=0$

$x=0\text{lub}x=-6$

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$\text{f)}-4x^4+4x^3-x^2=0\mid \cdot \left(-1\right)$

$4x^4-4x^3+x^2=0$

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

$x^2{\left(2x-1\right)}^2=0$

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

$x=0\text{lub}x=\frac{1}{2}$