0=-2a^2-12a-16

Solution for 0=-2a^2-12a-16 equation:

Simplifying
0 = -2a2 + -12a + -16

Reorder the terms:
0 = -16 + -12a + -2a2

Solving
0 = -16 + -12a + -2a2

Solving for variable 'a'.

Combine like terms: 0 + 16 = 16
16 + 12a + 2a2 = -16 + -12a + -2a2 + 16 + 12a + 2a2

Reorder the terms:
16 + 12a + 2a2 = -16 + 16 + -12a + 12a + -2a2 + 2a2

Combine like terms: -16 + 16 = 0
16 + 12a + 2a2 = 0 + -12a + 12a + -2a2 + 2a2
16 + 12a + 2a2 = -12a + 12a + -2a2 + 2a2

Combine like terms: -12a + 12a = 0
16 + 12a + 2a2 = 0 + -2a2 + 2a2
16 + 12a + 2a2 = -2a2 + 2a2

Combine like terms: -2a2 + 2a2 = 0
16 + 12a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 6a + a2) = 0

Factor a trinomial.
2((4 + a)(2 + a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + a)' equal to zero and attempt to solve:

Simplifying
4 + a = 0

Solving
4 + a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + a = 0 + -4
a = 0 + -4

Combine like terms: 0 + -4 = -4
a = -4

Simplifying
a = -4
Subproblem 2
Set the factor '(2 + a)' equal to zero and attempt to solve:

Simplifying
2 + a = 0

Solving
2 + a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + a = 0 + -2
a = 0 + -2

Combine like terms: 0 + -2 = -2
a = -2

Simplifying
a = -2
Solution
a = {-4, -2}