w^2+4wf-21f^2=

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Solution for w^2+4wf-21f^2= equation: 


Simplifying
w2 + 4wf + -21f2 = 0

Reorder the terms:
4fw + -21f2 + w2 = 0

Solving
4fw + -21f2 + w2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-7f + -1w)(3f + -1w) = 0


Subproblem 1
Set the factor '(-7f + -1w)' equal to zero and attempt to solve:

Simplifying
-7f + -1w = 0

Solving
-7f + -1w = 0

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

Add 'w' to each side of the equation.
-7f + -1w + w = 0 + w

Combine like terms: -1w + w = 0
-7f + 0 = 0 + w
-7f = 0 + w
Remove the zero:
-7f = w

Divide each side by '-7'.
f = -0.1428571429w

Simplifying
f = -0.1428571429w

Subproblem 2
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
Solution
f = {-0.1428571429w, 0.3333333333w}

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