(5v-6f)(5v+5f)=0

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Solution for (5v-6f)(5v+5f)=0 equation: 


Simplifying
(5v + -6f)(5v + 5f) = 0

Reorder the terms:
(-6f + 5v)(5v + 5f) = 0

Reorder the terms:
(-6f + 5v)(5f + 5v) = 0

Multiply (-6f + 5v) * (5f + 5v)
(-6f * (5f + 5v) + 5v * (5f + 5v)) = 0
((5f * -6f + 5v * -6f) + 5v * (5f + 5v)) = 0

Reorder the terms:
((-30fv + -30f2) + 5v * (5f + 5v)) = 0
((-30fv + -30f2) + 5v * (5f + 5v)) = 0
(-30fv + -30f2 + (5f * 5v + 5v * 5v)) = 0
(-30fv + -30f2 + (25fv + 25v2)) = 0

Reorder the terms:
(-30fv + 25fv + -30f2 + 25v2) = 0

Combine like terms: -30fv + 25fv = -5fv
(-5fv + -30f2 + 25v2) = 0

Solving
-5fv + -30f2 + 25v2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-1fv + -6f2 + 5v2) = 0

Factor a trinomial.
5((-1f + -1v)(6f + -5v)) = 0

Ignore the factor 5.

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

Simplifying
-1f + -1v = 0

Solving
-1f + -1v = 0

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

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

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

Divide each side by '-1'.
f = -1v

Simplifying
f = -1v

Subproblem 2
Set the factor '(6f + -5v)' equal to zero and attempt to solve:

Simplifying
6f + -5v = 0

Solving
6f + -5v = 0

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

Add '5v' to each side of the equation.
6f + -5v + 5v = 0 + 5v

Combine like terms: -5v + 5v = 0
6f + 0 = 0 + 5v
6f = 0 + 5v
Remove the zero:
6f = 5v

Divide each side by '6'.
f = 0.8333333333v

Simplifying
f = 0.8333333333v
Solution
f = {-1v, 0.8333333333v}

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