16r^4-f^4=

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Solution for 16r^4-f^4= equation: 


Simplifying
16r4 + -1f4 = 0

Reorder the terms:
-1f4 + 16r4 = 0

Solving
-1f4 + 16r4 = 0

Solving for variable 'f'.

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

Add '-16r4' to each side of the equation.
-1f4 + 16r4 + -16r4 = 0 + -16r4

Combine like terms: 16r4 + -16r4 = 0
-1f4 + 0 = 0 + -16r4
-1f4 = 0 + -16r4
Remove the zero:
-1f4 = -16r4

Divide each side by '-1'.
f4 = 16r4

Simplifying
f4 = 16r4

Combine like terms: 16r4 + -16r4 = 0
f4 + -16r4 = 0

Factor a difference between two squares.
(f2 + 4r2)(f2 + -4r2) = 0

Factor a difference between two squares.
(f2 + 4r2)((f + 2r)(f + -2r)) = 0


Subproblem 1
Set the factor '(f2 + 4r2)' equal to zero and attempt to solve:

Simplifying
f2 + 4r2 = 0

Solving
f2 + 4r2 = 0

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

Add '-4r2' to each side of the equation.
f2 + 4r2 + -4r2 = 0 + -4r2

Combine like terms: 4r2 + -4r2 = 0
f2 + 0 = 0 + -4r2
f2 = 0 + -4r2
Remove the zero:
f2 = -4r2

Simplifying
f2 = -4r2

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 '(f + 2r)' equal to zero and attempt to solve:

Simplifying
f + 2r = 0

Solving
f + 2r = 0

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

Add '-2r' to each side of the equation.
f + 2r + -2r = 0 + -2r

Combine like terms: 2r + -2r = 0
f + 0 = 0 + -2r
f = 0 + -2r
Remove the zero:
f = -2r

Simplifying
f = -2r

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

Simplifying
f + -2r = 0

Solving
f + -2r = 0

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

Add '2r' to each side of the equation.
f + -2r + 2r = 0 + 2r

Combine like terms: -2r + 2r = 0
f + 0 = 0 + 2r
f = 0 + 2r
Remove the zero:
f = 2r

Simplifying
f = 2r
Solution
f = {-2r, 2r}

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