#### Answer

Answer:
(a + 1)(a - 6)

#### Work Step by Step

$-2a^{2}$ + 10a +12
First, take out -2 common:
$-2a^{2}$ + 10a +12 = -2($a^{2}$ - 5a - 6) ....(since (-2)(-5) = 10 and (-2)(-6) = 12)
Now we need two numbers such that their sum is -5 and their product is -6.
Thus the two numbers are -6 and 1.
Check the two numbers are right:
Sum = -6 + 1 = -5
Product = (-6)(1) = (-6).
Thus,
$a^{2}$ - 5a - 6 = $a^{2}$ - 6a + a - 6
= a(a -6) + 1(a - 6)
=(a + 1)(a - 6).