v^2+13vf+40f^2=

Solution for v^2+13vf+40f^2= equation:

Simplifying
v2 + 13vf + 40f2 = 0

Reorder the terms:
13fv + 40f2 + v2 = 0

Solving
13fv + 40f2 + v2 = 0

Solving for variable 'f'.

Factor a trinomial.
(8f + v)(5f + v) = 0

Subproblem 1
Set the factor '(8f + v)' equal to zero and attempt to solve:

Simplifying
8f + v = 0

Solving
8f + v = 0

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

Add '-1v' to each side of the equation.
8f + v + -1v = 0 + -1v

Combine like terms: v + -1v = 0
8f + 0 = 0 + -1v
8f = 0 + -1v
Remove the zero:
8f = -1v

Divide each side by '8'.
f = -0.125v

Simplifying
f = -0.125v
Subproblem 2
Set the factor '(5f + v)' equal to zero and attempt to solve:

Simplifying
5f + v = 0

Solving
5f + v = 0

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

Add '-1v' to each side of the equation.
5f + v + -1v = 0 + -1v

Combine like terms: v + -1v = 0
5f + 0 = 0 + -1v
5f = 0 + -1v
Remove the zero:
5f = -1v

Divide each side by '5'.
f = -0.2v

Simplifying
f = -0.2v
Solution
f = {-0.125v, -0.2v}