15x^2-19xy=-6y^2

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Solution for 15x^2-19xy=-6y^2 equation:


Simplifying
15x2 + -19xy = -6y2

Reorder the terms:
-19xy + 15x2 = -6y2

Solving
-19xy + 15x2 = -6y2

Solving for variable 'x'.

Combine like terms: -6y2 + 6y2 = 0
-19xy + 15x2 + 6y2 = 0

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


Subproblem 1
Set the factor '(3x + -2y)' equal to zero and attempt to solve:

Simplifying
3x + -2y = 0

Solving
3x + -2y = 0

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

Add '2y' to each side of the equation.
3x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
3x + 0 = 0 + 2y
3x = 0 + 2y
Remove the zero:
3x = 2y

Divide each side by '3'.
x = 0.6666666667y

Simplifying
x = 0.6666666667y

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

Simplifying
5x + -3y = 0

Solving
5x + -3y = 0

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

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

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

Divide each side by '5'.
x = 0.6y

Simplifying
x = 0.6y
Solution
x = {0.6666666667y, 0.6y}

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