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

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

Simplifying
0 = x2 + 4ax + -5a2

Reorder the terms:
0 = 4ax + -5a2 + x2

Solving
0 = 4ax + -5a2 + x2

Solving for variable 'a'.
Remove the zero:
-4ax + 5a2 + -1x2 = 4ax + -5a2 + x2 + -4ax + 5a2 + -1x2

Reorder the terms:
-4ax + 5a2 + -1x2 = 4ax + -4ax + -5a2 + 5a2 + x2 + -1x2

Combine like terms: 4ax + -4ax = 0
-4ax + 5a2 + -1x2 = 0 + -5a2 + 5a2 + x2 + -1x2
-4ax + 5a2 + -1x2 = -5a2 + 5a2 + x2 + -1x2

Combine like terms: -5a2 + 5a2 = 0
-4ax + 5a2 + -1x2 = 0 + x2 + -1x2
-4ax + 5a2 + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4ax + 5a2 + -1x2 = 0

Factor a trinomial.
(a + -1x)(5a + x) = 0

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

Simplifying
a + -1x = 0

Solving
a + -1x = 0

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

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

Combine like terms: -1x + x = 0
a + 0 = 0 + x
a = 0 + x
Remove the zero:
a = x

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

Simplifying
5a + x = 0

Solving
5a + x = 0

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

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

Combine like terms: x + -1x = 0
5a + 0 = 0 + -1x
5a = 0 + -1x
Remove the zero:
5a = -1x

Divide each side by '5'.
a = -0.2x

Simplifying
a = -0.2x
Solution
a = {x, -0.2x}