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