a^2x^2-4ax-5=0

Solution for a^2x^2-4ax-5=0 equation:

Simplifying
a2x2 + -4ax + -5 = 0

Reorder the terms:
-5 + -4ax + a2x2 = 0

Solving
-5 + -4ax + a2x2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1 + -1ax)(5 + -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 = -1x-1

Simplifying
a = -1x-1
Subproblem 2
Set the factor '(5 + -1ax)' equal to zero and attempt to solve:

Simplifying
5 + -1ax = 0

Solving
5 + -1ax = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1ax = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1ax = 0 + -5
-1ax = 0 + -5

Combine like terms: 0 + -5 = -5
-1ax = -5

Divide each side by '-1x'.
a = 5x-1

Simplifying
a = 5x-1
Solution
a = {-1x-1, 5x-1}