2a^2x^2-abx-3b^2=0

Solution for 2a^2x^2-abx-3b^2=0 equation:

Simplifying
2a2x2 + -1abx + -3b2 = 0

Reorder the terms:
-1abx + 2a2x2 + -3b2 = 0

Solving
-1abx + 2a2x2 + -3b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2ax + -3b)(ax + b) = 0

Subproblem 1
Set the factor '(2ax + -3b)' equal to zero and attempt to solve:

Simplifying
2ax + -3b = 0

Solving
2ax + -3b = 0

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

Add '3b' to each side of the equation.
2ax + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
2ax + 0 = 0 + 3b
2ax = 0 + 3b
Remove the zero:
2ax = 3b

Divide each side by '2x'.
a = 1.5bx-1

Simplifying
a = 1.5bx-1
Subproblem 2
Set the factor '(ax + b)' equal to zero and attempt to solve:

Simplifying
ax + b = 0

Solving
ax + b = 0

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

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

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

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

Simplifying
a = -1bx-1
Solution
a = {1.5bx-1, -1bx-1}