a^2x^2+2b^2=3ab

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

Simplifying
a2x2 + 2b2 = 3ab

Solving
a2x2 + 2b2 = 3ab

Solving for variable 'a'.

Reorder the terms:
-3ab + a2x2 + 2b2 = 3ab + -3ab

Combine like terms: 3ab + -3ab = 0
-3ab + a2x2 + 2b2 = 0

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

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

Simplifying
ax + -2b = 0

Solving
ax + -2b = 0

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

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

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

Divide each side by 'x'.
a = 2bx-1

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

Simplifying
ax + -1b = 0

Solving
ax + -1b = 0

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

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

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

Divide each side by 'x'.
a = bx-1

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