e^2+4ef-21f^2=0

Solution for e^2+4ef-21f^2=0 equation:

Simplifying
e2 + 4ef + -21f2 = 0

Reorder the terms:
4ef + e2 + -21f2 = 0

Solving
4ef + e2 + -21f2 = 0

Solving for variable 'e'.

Factor a trinomial.
(e + -3f)(e + 7f) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(e + 7f)' equal to zero and attempt to solve:

Simplifying
e + 7f = 0

Solving
e + 7f = 0

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

Add '-7f' to each side of the equation.
e + 7f + -7f = 0 + -7f

Combine like terms: 7f + -7f = 0
e + 0 = 0 + -7f
e = 0 + -7f
Remove the zero:
e = -7f

Simplifying
e = -7f
Solution
e = {3f, -7f}