a^2-3ab+2b^2=0

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

Simplifying
a2 + -3ab + 2b2 = 0

Reorder the terms:
-3ab + a2 + 2b2 = 0

Solving
-3ab + a2 + 2b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -2b)(a + -1b) = 0

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

Simplifying
a + -1b = 0

Solving
a + -1b = 0

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

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

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

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