0=27x^2-186xy-240y^2

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Solution for 0=27x^2-186xy-240y^2 equation: 


Simplifying
0 = 27x2 + -186xy + -240y2

Reorder the terms:
0 = -186xy + 27x2 + -240y2

Solving
0 = -186xy + 27x2 + -240y2

Solving for variable 'x'.
Remove the zero:
186xy + -27x2 + 240y2 = -186xy + 27x2 + -240y2 + 186xy + -27x2 + 240y2

Reorder the terms:
186xy + -27x2 + 240y2 = -186xy + 186xy + 27x2 + -27x2 + -240y2 + 240y2

Combine like terms: -186xy + 186xy = 0
186xy + -27x2 + 240y2 = 0 + 27x2 + -27x2 + -240y2 + 240y2
186xy + -27x2 + 240y2 = 27x2 + -27x2 + -240y2 + 240y2

Combine like terms: 27x2 + -27x2 = 0
186xy + -27x2 + 240y2 = 0 + -240y2 + 240y2
186xy + -27x2 + 240y2 = -240y2 + 240y2

Combine like terms: -240y2 + 240y2 = 0
186xy + -27x2 + 240y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(62xy + -9x2 + 80y2) = 0

Factor a trinomial.
3((-9x + -10y)(x + -8y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-9x + -10y)' equal to zero and attempt to solve:

Simplifying
-9x + -10y = 0

Solving
-9x + -10y = 0

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

Add '10y' to each side of the equation.
-9x + -10y + 10y = 0 + 10y

Combine like terms: -10y + 10y = 0
-9x + 0 = 0 + 10y
-9x = 0 + 10y
Remove the zero:
-9x = 10y

Divide each side by '-9'.
x = -1.111111111y

Simplifying
x = -1.111111111y

Subproblem 2
Set the factor '(x + -8y)' equal to zero and attempt to solve:

Simplifying
x + -8y = 0

Solving
x + -8y = 0

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

Add '8y' to each side of the equation.
x + -8y + 8y = 0 + 8y

Combine like terms: -8y + 8y = 0
x + 0 = 0 + 8y
x = 0 + 8y
Remove the zero:
x = 8y

Simplifying
x = 8y
Solution
x = {-1.111111111y, 8y}

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