a^2+9ab+18b^2=0

Solution for a^2+9ab+18b^2=0 equation:

Simplifying
a2 + 9ab + 18b2 = 0

Reorder the terms:
9ab + a2 + 18b2 = 0

Solving
9ab + a2 + 18b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + 3b)(a + 6b) = 0

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

Simplifying
a + 3b = 0

Solving
a + 3b = 0

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

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

Combine like terms: 3b + -3b = 0
a + 0 = 0 + -3b
a = 0 + -3b
Remove the zero:
a = -3b

Simplifying
a = -3b
Subproblem 2
Set the factor '(a + 6b)' equal to zero and attempt to solve:

Simplifying
a + 6b = 0

Solving
a + 6b = 0

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

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

Combine like terms: 6b + -6b = 0
a + 0 = 0 + -6b
a = 0 + -6b
Remove the zero:
a = -6b

Simplifying
a = -6b
Solution
a = {-3b, -6b}