k^2+6kf-40f^2=0

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Solution for k^2+6kf-40f^2=0 equation: 


Simplifying
k2 + 6kf + -40f2 = 0

Reorder the terms:
6fk + -40f2 + k2 = 0

Solving
6fk + -40f2 + k2 = 0

Solving for variable 'f'.

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


Subproblem 1
Set the factor '(-10f + -1k)' equal to zero and attempt to solve:

Simplifying
-10f + -1k = 0

Solving
-10f + -1k = 0

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

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

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

Divide each side by '-10'.
f = -0.1k

Simplifying
f = -0.1k

Subproblem 2
Set the factor '(4f + -1k)' equal to zero and attempt to solve:

Simplifying
4f + -1k = 0

Solving
4f + -1k = 0

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

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

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

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

Simplifying
f = 0.25k
Solution
f = {-0.1k, 0.25k}

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