min(a^2+6a+9)=0

Solution for min(a^2+6a+9)=0 equation:

Simplifying
min(a2 + 6a + 9) = 0

Reorder the terms:
imn(9 + 6a + a2) = 0
(9 * imn + 6a * imn + a2 * imn) = 0

Reorder the terms:
(6aimn + a2imn + 9imn) = 0
(6aimn + a2imn + 9imn) = 0

Solving
6aimn + a2imn + 9imn = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'imn'.
imn(6a + a2 + 9) = 0

Factor a trinomial.
imn((a + 3)(a + 3)) = 0

Subproblem 1
Set the factor 'imn' equal to zero and attempt to solve:

Simplifying
imn = 0

Solving
imn = 0

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

Add '-1imn' to each side of the equation.
imn + -1imn = 0 + -1imn
Remove the zero:
0 = -1imn

Simplifying
0 = -1imn

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(a + 3)' equal to zero and attempt to solve:

Simplifying
a + 3 = 0

Reorder the terms:
3 + a = 0

Solving
3 + a = 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 + a = 0 + -3

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

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

Simplifying
a = -3
Subproblem 3
Set the factor '(a + 3)' equal to zero and attempt to solve:

Simplifying
a + 3 = 0

Reorder the terms:
3 + a = 0

Solving
3 + a = 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 + a = 0 + -3

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

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

Simplifying
a = -3
Solution
a = {-3, -3}