$\text{a)}\left(x-5\right)\left(x+3\right)=0$  

$x-5=0\vee x+3=0$  

$x=5\vee x=-3$  

$x\in \left\{-3,5\right\}$  

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$\text{b)}{x}^2+4x=0$  

$x\left(x+4\right)=0$  

$x=0\vee x+4=0$  

$x=0\vee x=-4$  

$x\in \left\{-4,0\right\}$  

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$\text{c)}5x-x^2=0$  

$x\left(5-x\right)=0$  

$x=0\vee 5-x=0$  

$x=0\vee x=5$  

$x\in \left\{0,5\right\}$  

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$\text{d)}2x^2-12x=0\mid :2$  

$x^2-6x=0$  

$x\left(x-6\right)=0$  

$x=0\vee x-6=0$  

$x=0\vee x=6$  

$x\in \left\{0,6\right\}$  

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$\text{e)}4x^2+6x=0\mid :2$  

$2x^2+3x=0$  

$x\left(2x+3\right)=0$  

$x=0\vee 2x+3=0$  

$x=0\vee 2x=-3\mid :2$  

$x=0\vee x=-\frac{3}{2}$  

$x\in \left\{-\frac{3}{2},0\right\}$  

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$\text{f)}7x+14x^2=0\mid :7$  

$x+2x^2=0$  

$x\left(1+2x\right)=0$  

$x=0\vee 1+2x=0$  

$x=0\vee 2x=-1\mid :2$  

$x=0\vee x=-\frac{1}{2}$  

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

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$\text{g)}7x=x^2$  

$7x-x^2=0$  

$x\left(7-x\right)=0$  

$x=0\vee 7-x=0$  

$x=0\vee x=7$  

$x\in \left\{0,7\right\}$  

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$\text{h)}5x=-20x^2\mid :5$  

$x=-4x^2$  

$x+4x^2=0$  

$x\left(1+4x\right)=0$  

$x=0\vee 1+4x=0$  

$x=0\vee 4x=-1\mid :4$  

$x=0\vee x=-\frac{1}{4}$  

$x\in \left\{-\frac{1}{4},0\right\}$  

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$\text{i)}-2x^2=-8x\mid :\left(-2\right)$   

$x^2=4x$  

$x^2-4x=0$  

$x\left(x-4\right)=0$  

$x=0\vee x-4=0$  

$x=0\vee x=4$  

$x\in \left\{0,4\right\}$