45x^2+57xy-30y^2=

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Solution for 45x^2+57xy-30y^2= equation: 


Simplifying
45x2 + 57xy + -30y2 = 0

Reorder the terms:
57xy + 45x2 + -30y2 = 0

Solving
57xy + 45x2 + -30y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(19xy + 15x2 + -10y2) = 0

Factor a trinomial.
3((5x + -2y)(3x + 5y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(5x + -2y)' equal to zero and attempt to solve:

Simplifying
5x + -2y = 0

Solving
5x + -2y = 0

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

Add '2y' to each side of the equation.
5x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
5x + 0 = 0 + 2y
5x = 0 + 2y
Remove the zero:
5x = 2y

Divide each side by '5'.
x = 0.4y

Simplifying
x = 0.4y

Subproblem 2
Set the factor '(3x + 5y)' equal to zero and attempt to solve:

Simplifying
3x + 5y = 0

Solving
3x + 5y = 0

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

Add '-5y' to each side of the equation.
3x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
3x + 0 = 0 + -5y
3x = 0 + -5y
Remove the zero:
3x = -5y

Divide each side by '3'.
x = -1.666666667y

Simplifying
x = -1.666666667y
Solution
x = {0.4y, -1.666666667y}

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