v^2+6vf-16f^2=0

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Solution for v^2+6vf-16f^2=0 equation: 


Simplifying
v2 + 6vf + -16f2 = 0

Reorder the terms:
6fv + -16f2 + v2 = 0

Solving
6fv + -16f2 + v2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-8f + -1v)(2f + -1v) = 0


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

Simplifying
-8f + -1v = 0

Solving
-8f + -1v = 0

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

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

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

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

Simplifying
f = -0.125v

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

Simplifying
2f + -1v = 0

Solving
2f + -1v = 0

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

Add 'v' to each side of the equation.
2f + -1v + v = 0 + v

Combine like terms: -1v + v = 0
2f + 0 = 0 + v
2f = 0 + v
Remove the zero:
2f = v

Divide each side by '2'.
f = 0.5v

Simplifying
f = 0.5v
Solution
f = {-0.125v, 0.5v}

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