(u+v)(u+v)=0

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Solution for (u+v)(u+v)=0 equation: 


Simplifying
(u + v)(u + v) = 0

Multiply (u + v) * (u + v)
(u(u + v) + v(u + v)) = 0
((u * u + v * u) + v(u + v)) = 0

Reorder the terms:
((uv + u2) + v(u + v)) = 0
((uv + u2) + v(u + v)) = 0
(uv + u2 + (u * v + v * v)) = 0
(uv + u2 + (uv + v2)) = 0

Reorder the terms:
(uv + uv + u2 + v2) = 0

Combine like terms: uv + uv = 2uv
(2uv + u2 + v2) = 0

Solving
2uv + u2 + v2 = 0

Solving for variable 'u'.

Factor a trinomial.
(u + v)(u + v) = 0


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

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

Simplifying
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
Solution
u = {-1v, -1v}

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