w^2+5wf-36f^2=

Solution for w^2+5wf-36f^2= equation:

Simplifying
w2 + 5wf + -36f2 = 0

Reorder the terms:
5fw + -36f2 + w2 = 0

Solving
5fw + -36f2 + w2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-9f + -1w)(4f + -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 '(4f + -1w)' equal to zero and attempt to solve:

Simplifying
4f + -1w = 0

Solving
4f + -1w = 0

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

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

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

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

Simplifying
f = 0.25w
Solution
f = {-0.1111111111w, 0.25w}