(u-4vy)(u+vy)=

Solution for (u-4vy)(u+vy)= equation:

Simplifying
(u + -4vy)(u + vy) = 0

Multiply (u + -4vy) * (u + vy)
(u(u + vy) + -4vy * (u + vy)) = 0
((u * u + vy * u) + -4vy * (u + vy)) = 0

Reorder the terms:
((uvy + u2) + -4vy * (u + vy)) = 0
((uvy + u2) + -4vy * (u + vy)) = 0
(uvy + u2 + (u * -4vy + vy * -4vy)) = 0
(uvy + u2 + (-4uvy + -4v2y2)) = 0

Reorder the terms:
(uvy + -4uvy + u2 + -4v2y2) = 0

Combine like terms: uvy + -4uvy = -3uvy
(-3uvy + u2 + -4v2y2) = 0

Solving
-3uvy + u2 + -4v2y2 = 0

Solving for variable 'u'.

Factor a trinomial.
(u + -4vy)(u + vy) = 0

Subproblem 1
Set the factor '(u + -4vy)' equal to zero and attempt to solve:

Simplifying
u + -4vy = 0

Solving
u + -4vy = 0

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

Add '4vy' to each side of the equation.
u + -4vy + 4vy = 0 + 4vy

Combine like terms: -4vy + 4vy = 0
u + 0 = 0 + 4vy
u = 0 + 4vy
Remove the zero:
u = 4vy

Simplifying
u = 4vy
Subproblem 2
Set the factor '(u + vy)' equal to zero and attempt to solve:

Simplifying
u + vy = 0

Solving
u + vy = 0

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

Add '-1vy' to each side of the equation.
u + vy + -1vy = 0 + -1vy

Combine like terms: vy + -1vy = 0
u + 0 = 0 + -1vy
u = 0 + -1vy
Remove the zero:
u = -1vy

Simplifying
u = -1vy
Solution
u = {4vy, -1vy}