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

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

Simplifying
x2 + 5ax + 4a2 = 0

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

Solving
5ax + 4a2 + x2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4a + x)(a + x) = 0

Subproblem 1
Set the factor '(4a + x)' equal to zero and attempt to solve:

Simplifying
4a + x = 0

Solving
4a + x = 0

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

Add '-1x' to each side of the equation.
4a + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
4a + 0 = 0 + -1x
4a = 0 + -1x
Remove the zero:
4a = -1x

Divide each side by '4'.
a = -0.25x

Simplifying
a = -0.25x
Subproblem 2
Set the factor '(a + x)' equal to zero and attempt to solve:

Simplifying
a + x = 0

Solving
a + x = 0

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

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

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

Simplifying
a = -1x
Solution
a = {-0.25x, -1x}