7U^4-7U^2V^2=0

Solution for 7U^4-7U^2V^2=0 equation:

Simplifying
7U4 + -7U2V2 = 0

Reorder the terms:
-7U2V2 + 7U4 = 0

Solving
-7U2V2 + 7U4 = 0

Solving for variable 'U'.

Factor out the Greatest Common Factor (GCF), '7U2'.
7U2(-1V2 + U2) = 0

Factor a difference between two squares.
7U2((V + U)(-1V + U)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor 'U2' equal to zero and attempt to solve:

Simplifying
U2 = 0

Solving
U2 = 0

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

Simplifying
U2 = 0

Take the square root of each side:
U = {0}
Subproblem 2
Set the factor '(V + U)' equal to zero and attempt to solve:

Simplifying
V + U = 0

Reorder the terms:
U + V = 0

Solving
U + V = 0

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

Add '-1V' to each side of the equation.
U + V + -1V = 0 + -1V

Combine like terms: V + -1V = 0
U + 0 = 0 + -1V
U = 0 + -1V
Remove the zero:
U = -1V

Simplifying
U = -1V
Subproblem 3
Set the factor '(-1V + U)' equal to zero and attempt to solve:

Simplifying
-1V + U = 0

Reorder the terms:
U + -1V = 0

Solving
U + -1V = 0

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

Add 'V' to each side of the equation.
U + -1V + V = 0 + V

Combine like terms: -1V + V = 0
U + 0 = 0 + V
U = 0 + V
Remove the zero:
U = V

Simplifying
U = V
Solution
U = {0, -1V, V}