a^2x^2-5abx+4b^2=0

Solution for a^2x^2-5abx+4b^2=0 equation:

Simplifying
a2x2 + -5abx + 4b2 = 0

Reorder the terms:
-5abx + a2x2 + 4b2 = 0

Solving
-5abx + a2x2 + 4b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(ax + -4b)(ax + -1b) = 0

Subproblem 1
Set the factor '(ax + -4b)' equal to zero and attempt to solve:

Simplifying
ax + -4b = 0

Solving
ax + -4b = 0

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

Add '4b' to each side of the equation.
ax + -4b + 4b = 0 + 4b

Combine like terms: -4b + 4b = 0
ax + 0 = 0 + 4b
ax = 0 + 4b
Remove the zero:
ax = 4b

Divide each side by 'x'.
a = 4bx-1

Simplifying
a = 4bx-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 = {4bx-1, bx-1}