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 + -6b)(a + -3b) = 0

Subproblem 1
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
Subproblem 2
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
Solution
a = {6b, 3b}