w^2+12wf+27f^2=0

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Solution for w^2+12wf+27f^2=0 equation: 


Simplifying
w2 + 12wf + 27f2 = 0

Reorder the terms:
12fw + 27f2 + w2 = 0

Solving
12fw + 27f2 + w2 = 0

Solving for variable 'f'.

Factor a trinomial.
(9f + w)(3f + w) = 0


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

Simplifying
9f + w = 0

Solving
9f + w = 0

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

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

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

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

Simplifying
f = -0.1111111111w

Subproblem 2
Set the factor '(3f + w)' equal to zero and attempt to solve:

Simplifying
3f + w = 0

Solving
3f + w = 0

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

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

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

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

Simplifying
f = -0.3333333333w
Solution
f = {-0.1111111111w, -0.3333333333w}

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