w^2-7wf-30f^2=0

Solution for w^2-7wf-30f^2=0 equation:

Simplifying
w2 + -7wf + -30f2 = 0

Reorder the terms:
-7fw + -30f2 + w2 = 0

Solving
-7fw + -30f2 + w2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-3f + -1w)(10f + -1w) = 0

Subproblem 1
Set the factor '(-3f + -1w)' equal to zero and attempt to solve:

Simplifying
-3f + -1w = 0

Solving
-3f + -1w = 0

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

Add 'w' to each side of the equation.
-3f + -1w + w = 0 + w

Combine like terms: -1w + w = 0
-3f + 0 = 0 + w
-3f = 0 + w
Remove the zero:
-3f = w

Divide each side by '-3'.
f = -0.3333333333w

Simplifying
f = -0.3333333333w
Subproblem 2
Set the factor '(10f + -1w)' equal to zero and attempt to solve:

Simplifying
10f + -1w = 0

Solving
10f + -1w = 0

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

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

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

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

Simplifying
f = 0.1w
Solution
f = {-0.3333333333w, 0.1w}