12a^2+24a+9=0

Solution for 12a^2+24a+9=0 equation:

Simplifying
12a2 + 24a + 9 = 0

Reorder the terms:
9 + 24a + 12a2 = 0

Solving
9 + 24a + 12a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 8a + 4a2) = 0

Factor a trinomial.
3((3 + 2a)(1 + 2a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + 2a)' equal to zero and attempt to solve:

Simplifying
3 + 2a = 0

Solving
3 + 2a = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2a = 0 + -3
2a = 0 + -3

Combine like terms: 0 + -3 = -3
2a = -3

Divide each side by '2'.
a = -1.5

Simplifying
a = -1.5
Subproblem 2
Set the factor '(1 + 2a)' equal to zero and attempt to solve:

Simplifying
1 + 2a = 0

Solving
1 + 2a = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2a = 0 + -1
2a = 0 + -1

Combine like terms: 0 + -1 = -1
2a = -1

Divide each side by '2'.
a = -0.5

Simplifying
a = -0.5
Solution
a = {-1.5, -0.5}