w^2+7wf-18f^2=0

Solution for w^2+7wf-18f^2=0 equation:

Simplifying
w2 + 7wf + -18f2 = 0

Reorder the terms:
7fw + -18f2 + w2 = 0

Solving
7fw + -18f2 + w2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-9f + -1w)(2f + -1w) = 0

Subproblem 1
Set the factor '(-9f + -1w)' equal to zero and attempt to solve:

Simplifying
-9f + -1w = 0

Solving
-9f + -1w = 0

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

Add 'w' to each side of the equation.
-9f + -1w + w = 0 + w

Combine like terms: -1w + w = 0
-9f + 0 = 0 + w
-9f = 0 + w
Remove the zero:
-9f = w

Divide each side by '-9'.
f = -0.1111111111w

Simplifying
f = -0.1111111111w
Subproblem 2
Set the factor '(2f + -1w)' equal to zero and attempt to solve:

Simplifying
2f + -1w = 0

Solving
2f + -1w = 0

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

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

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

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

Simplifying
f = 0.5w
Solution
f = {-0.1111111111w, 0.5w}