a^2x^2-3ax+2=0

Solution for a^2x^2-3ax+2=0 equation:

Simplifying
a2x2 + -3ax + 2 = 0

Reorder the terms:
2 + -3ax + a2x2 = 0

Solving
2 + -3ax + a2x2 = 0

Solving for variable 'a'.

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

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

Simplifying
1 + -1ax = 0

Solving
1 + -1ax = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1ax = 0 + -1
-1ax = 0 + -1

Combine like terms: 0 + -1 = -1
-1ax = -1

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

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

Simplifying
2 + -1ax = 0

Solving
2 + -1ax = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1ax = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1ax = 0 + -2
-1ax = 0 + -2

Combine like terms: 0 + -2 = -2
-1ax = -2

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

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