15x^2-12xy-25xy+20y^2=0

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Solution for 15x^2-12xy-25xy+20y^2=0 equation:


Simplifying
15x2 + -12xy + -25xy + 20y2 = 0

Reorder the terms:
-12xy + -25xy + 15x2 + 20y2 = 0

Combine like terms: -12xy + -25xy = -37xy
-37xy + 15x2 + 20y2 = 0

Solving
-37xy + 15x2 + 20y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + -5y)(5x + -4y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5x + -4y)' equal to zero and attempt to solve:

Simplifying
5x + -4y = 0

Solving
5x + -4y = 0

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

Add '4y' to each side of the equation.
5x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
5x + 0 = 0 + 4y
5x = 0 + 4y
Remove the zero:
5x = 4y

Divide each side by '5'.
x = 0.8y

Simplifying
x = 0.8y
Solution
x = {1.666666667y, 0.8y}

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