(2u+4vy^2)(u+2vy^2)=0

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Solution for (2u+4vy^2)(u+2vy^2)=0 equation: 


Simplifying
(2u + 4vy2)(u + 2vy2) = 0

Multiply (2u + 4vy2) * (u + 2vy2)
(2u * (u + 2vy2) + 4vy2 * (u + 2vy2)) = 0
((u * 2u + 2vy2 * 2u) + 4vy2 * (u + 2vy2)) = 0

Reorder the terms:
((4uvy2 + 2u2) + 4vy2 * (u + 2vy2)) = 0
((4uvy2 + 2u2) + 4vy2 * (u + 2vy2)) = 0
(4uvy2 + 2u2 + (u * 4vy2 + 2vy2 * 4vy2)) = 0
(4uvy2 + 2u2 + (4uvy2 + 8v2y4)) = 0

Reorder the terms:
(4uvy2 + 4uvy2 + 2u2 + 8v2y4) = 0

Combine like terms: 4uvy2 + 4uvy2 = 8uvy2
(8uvy2 + 2u2 + 8v2y4) = 0

Solving
8uvy2 + 2u2 + 8v2y4 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4uvy2 + u2 + 4v2y4) = 0

Factor a trinomial.
2((u + 2vy2)(u + 2vy2)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(u + 2vy2)' equal to zero and attempt to solve:

Simplifying
u + 2vy2 = 0

Solving
u + 2vy2 = 0

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

Add '-2vy2' to each side of the equation.
u + 2vy2 + -2vy2 = 0 + -2vy2

Combine like terms: 2vy2 + -2vy2 = 0
u + 0 = 0 + -2vy2
u = 0 + -2vy2
Remove the zero:
u = -2vy2

Simplifying
u = -2vy2

Subproblem 2
Set the factor '(u + 2vy2)' equal to zero and attempt to solve:

Simplifying
u + 2vy2 = 0

Solving
u + 2vy2 = 0

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

Add '-2vy2' to each side of the equation.
u + 2vy2 + -2vy2 = 0 + -2vy2

Combine like terms: 2vy2 + -2vy2 = 0
u + 0 = 0 + -2vy2
u = 0 + -2vy2
Remove the zero:
u = -2vy2

Simplifying
u = -2vy2
Solution
u = {-2vy2, -2vy2}

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