$5{a}^{2}+a-10a-2=0$
Factor out $a$ from the expression$a \times \left( 5a+1 \right)-10a-2=0$
Factor out $-2$ from the expression$a \times \left( 5a+1 \right)-2\left( 5a+1 \right)=0$
Factor out $5a+1$ from the expression$\left( 5a+1 \right) \times \left( a-2 \right)=0$
When the product of factors equals $0$, at least one factor is $0$$\begin{array} { l }5a+1=0,\\a-2=0\end{array}$
Solve the equation for $a$$\begin{array} { l }a=-\frac{ 1 }{ 5 },\\a-2=0\end{array}$
Solve the equation for $a$$\begin{array} { l }a=-\frac{ 1 }{ 5 },\\a=2\end{array}$
The equation has $2$ solutions$\begin{align*}&\begin{array} { l }a_1=-\frac{ 1 }{ 5 },& a_2=2\end{array} \\&\begin{array} { l }a_1=-0.2,& a_2=2\end{array}\end{align*}$