3(a^2+3ab+2b^2)=0

Solution for 3(a^2+3ab+2b^2)=0 equation:

Simplifying
3(a2 + 3ab + 2b2) = 0

Reorder the terms:
3(3ab + a2 + 2b2) = 0
(3ab * 3 + a2 * 3 + 2b2 * 3) = 0
(9ab + 3a2 + 6b2) = 0

Solving
9ab + 3a2 + 6b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3ab + a2 + 2b2) = 0

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

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

Simplifying
a + b = 0

Solving
a + b = 0

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

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

Combine like terms: b + -1b = 0
a + 0 = 0 + -1b
a = 0 + -1b
Remove the zero:
a = -1b

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

Simplifying
a + 2b = 0

Solving
a + 2b = 0

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

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

Combine like terms: 2b + -2b = 0
a + 0 = 0 + -2b
a = 0 + -2b
Remove the zero:
a = -2b

Simplifying
a = -2b
Solution
a = {-1b, -2b}