6x^2+80xy+200y^2=0

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Solution for 6x^2+80xy+200y^2=0 equation: 


Simplifying
6x2 + 80xy + 200y2 = 0

Reorder the terms:
80xy + 6x2 + 200y2 = 0

Solving
80xy + 6x2 + 200y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(40xy + 3x2 + 100y2) = 0

Factor a trinomial.
2((3x + 10y)(x + 10y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3x + 10y)' equal to zero and attempt to solve:

Simplifying
3x + 10y = 0

Solving
3x + 10y = 0

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

Add '-10y' to each side of the equation.
3x + 10y + -10y = 0 + -10y

Combine like terms: 10y + -10y = 0
3x + 0 = 0 + -10y
3x = 0 + -10y
Remove the zero:
3x = -10y

Divide each side by '3'.
x = -3.333333333y

Simplifying
x = -3.333333333y

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

Simplifying
x + 10y = 0

Solving
x + 10y = 0

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

Add '-10y' to each side of the equation.
x + 10y + -10y = 0 + -10y

Combine like terms: 10y + -10y = 0
x + 0 = 0 + -10y
x = 0 + -10y
Remove the zero:
x = -10y

Simplifying
x = -10y
Solution
x = {-3.333333333y, -10y}

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