e^2+4ef+3f^2=0

Solution for e^2+4ef+3f^2=0 equation:

Simplifying
e2 + 4ef + 3f2 = 0

Reorder the terms:
4ef + e2 + 3f2 = 0

Solving
4ef + e2 + 3f2 = 0

Solving for variable 'e'.

Factor a trinomial.
(e + f)(e + 3f) = 0

Subproblem 1
Set the factor '(e + f)' equal to zero and attempt to solve:

Simplifying
e + f = 0

Solving
e + f = 0

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

Add '-1f' to each side of the equation.
e + f + -1f = 0 + -1f

Combine like terms: f + -1f = 0
e + 0 = 0 + -1f
e = 0 + -1f
Remove the zero:
e = -1f

Simplifying
e = -1f
Subproblem 2
Set the factor '(e + 3f)' equal to zero and attempt to solve:

Simplifying
e + 3f = 0

Solving
e + 3f = 0

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

Add '-3f' to each side of the equation.
e + 3f + -3f = 0 + -3f

Combine like terms: 3f + -3f = 0
e + 0 = 0 + -3f
e = 0 + -3f
Remove the zero:
e = -3f

Simplifying
e = -3f
Solution
e = {-1f, -3f}