x^2+4bx-5b^2=0

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

Simplifying
x2 + 4bx + -5b2 = 0

Reorder the terms:
4bx + -5b2 + x2 = 0

Solving
4bx + -5b2 + x2 = 0

Solving for variable 'b'.

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

Subproblem 1
Set the factor '(-5b + -1x)' equal to zero and attempt to solve:

Simplifying
-5b + -1x = 0

Solving
-5b + -1x = 0

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

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

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

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

Simplifying
b = -0.2x
Subproblem 2
Set the factor '(b + -1x)' equal to zero and attempt to solve:

Simplifying
b + -1x = 0

Solving
b + -1x = 0

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

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

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

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