v^2+3vf-40f^2=0

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Solution for v^2+3vf-40f^2=0 equation: 


Simplifying
v2 + 3vf + -40f2 = 0

Reorder the terms:
3fv + -40f2 + v2 = 0

Solving
3fv + -40f2 + v2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-8f + -1v)(5f + -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 '(5f + -1v)' equal to zero and attempt to solve:

Simplifying
5f + -1v = 0

Solving
5f + -1v = 0

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

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

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

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

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

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