v^2-14vf+40f^2=0

Solution for v^2-14vf+40f^2=0 equation:

Simplifying
v2 + -14vf + 40f2 = 0

Reorder the terms:
-14fv + 40f2 + v2 = 0

Solving
-14fv + 40f2 + v2 = 0

Solving for variable 'f'.

Factor a trinomial.
(4f + -1v)(10f + -1v) = 0

Subproblem 1
Set the factor '(4f + -1v)' equal to zero and attempt to solve:

Simplifying
4f + -1v = 0

Solving
4f + -1v = 0

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

Add 'v' to each side of the equation.
4f + -1v + v = 0 + v

Combine like terms: -1v + v = 0
4f + 0 = 0 + v
4f = 0 + v
Remove the zero:
4f = v

Divide each side by '4'.
f = 0.25v

Simplifying
f = 0.25v
Subproblem 2
Set the factor '(10f + -1v)' equal to zero and attempt to solve:

Simplifying
10f + -1v = 0

Solving
10f + -1v = 0

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

Add 'v' to each side of the equation.
10f + -1v + v = 0 + v

Combine like terms: -1v + v = 0
10f + 0 = 0 + v
10f = 0 + v
Remove the zero:
10f = v

Divide each side by '10'.
f = 0.1v

Simplifying
f = 0.1v
Solution
f = {0.25v, 0.1v}