w^6+5(w^5)(f)-14(w^4)(f^2)=0

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Solution for w^6+5(w^5)(f)-14(w^4)(f^2)=0 equation: 


Simplifying
w6 + 5(w5)(f) + -14(w4)(f2) = 0

Multiply w5 * f
w6 + 5fw5 + -14(w4)(f2) = 0

Multiply w4 * f2
w6 + 5fw5 + -14f2w4 = 0

Reorder the terms:
5fw5 + -14f2w4 + w6 = 0

Solving
5fw5 + -14f2w4 + w6 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), 'w4'.
w4(5fw + -14f2 + w2) = 0

Factor a trinomial.
w4((-7f + -1w)(2f + -1w)) = 0


Subproblem 1
Set the factor 'w4' equal to zero and attempt to solve:

Simplifying
w4 = 0

Solving
w4 = 0

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

Add '-1w4' to each side of the equation.
w4 + -1w4 = 0 + -1w4
Remove the zero:
0 = -1w4

Simplifying
0 = -1w4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
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 3
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 = {-0.1428571429w, 0.5w}

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