If $(x+a)$ is a factor of $(2x^2+2ax+5x+10)$, find the value of $a.$

Given : $(x+a)$ is a factor of $2x^2+(2a+5)x+10$
which shows that one of the zeroes of the given polynomial is $-a$ 

Now, $x=-a$ satisfy the given polynomial

$2(-a{)}^2+(2a+5)(-a)+10=0$
$2a^2-2a^2-5a+10=0$
$5a=10$
$a=2$