x^2+3x=0
and
5x^2-8x-4=0
$\displaystyle x(x+3) = 0$. This means either $\displaystyle x=0$ or $\displaystyle x+3=0$.
Because 5 is prime it must be 5 x 1 for coefficients of x^2.5x^2-8x-4=0
Trying -2*2 for the -4 and manipulating gives
$\displaystyle (5x+2)(x-2)=0$
This will come naturally with practice