Solve each of the following quadratic equations:

We write, $6 x=x+5 x$ as $x^{2} \times 5=5 x^{2}=x \times 5 x$

$\therefore x^{2}+6 x+5=0$

$\Rightarrow x^{2}+x+5 x+5=0$

$\Rightarrow x(x+1)+5(x+1)=0$

$\Rightarrow(x+1)(x+5)=0$

$\Rightarrow x+1=0$ or $x+5=0$

$\Rightarrow x=-1$ or $x=-5$

Hence, the roots of the given equation are −1 and −5.