a^2x^2+abx-2b^2=0

Solution for a^2x^2+abx-2b^2=0 equation:

Simplifying
a2x2 + abx + -2b2 = 0

Reorder the terms:
abx + a2x2 + -2b2 = 0

Solving
abx + a2x2 + -2b2 = 0

Solving for variable 'a'.

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

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