u^2+5uv-50v^2=0

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Solution for u^2+5uv-50v^2=0 equation: 


Simplifying
u2 + 5uv + -50v2 = 0

Reorder the terms:
5uv + u2 + -50v2 = 0

Solving
5uv + u2 + -50v2 = 0

Solving for variable 'u'.

Factor a trinomial.
(u + -5v)(u + 10v) = 0


Subproblem 1
Set the factor '(u + -5v)' equal to zero and attempt to solve:

Simplifying
u + -5v = 0

Solving
u + -5v = 0

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

Add '5v' to each side of the equation.
u + -5v + 5v = 0 + 5v

Combine like terms: -5v + 5v = 0
u + 0 = 0 + 5v
u = 0 + 5v
Remove the zero:
u = 5v

Simplifying
u = 5v

Subproblem 2
Set the factor '(u + 10v)' equal to zero and attempt to solve:

Simplifying
u + 10v = 0

Solving
u + 10v = 0

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

Add '-10v' to each side of the equation.
u + 10v + -10v = 0 + -10v

Combine like terms: 10v + -10v = 0
u + 0 = 0 + -10v
u = 0 + -10v
Remove the zero:
u = -10v

Simplifying
u = -10v
Solution
u = {5v, -10v}

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