2a^2+8a+12=0

Solution for 2a^2+8a+12=0 equation:

Simplifying
2a2 + 8a + 12 = 0

Reorder the terms:
12 + 8a + 2a2 = 0

Solving
12 + 8a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 4a + a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 4a + a2)' equal to zero and attempt to solve:

Simplifying
6 + 4a + a2 = 0

Solving
6 + 4a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 4a + -6 + a2 = 0 + -6

Reorder the terms:
6 + -6 + 4a + a2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 4a + a2 = 0 + -6
4a + a2 = 0 + -6

Combine like terms: 0 + -6 = -6
4a + a2 = -6

The a term is 4a.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4a + 4 + a2 = -6 + 4

Reorder the terms:
4 + 4a + a2 = -6 + 4

Combine like terms: -6 + 4 = -2
4 + 4a + a2 = -2

Factor a perfect square on the left side:
(a + 2)(a + 2) = -2

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.