45x^2+57xy-30y^2=0

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Solution for 45x^2+57xy-30y^2=0 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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