-4x^2+4xy+15y^2=0

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Solution for -4x^2+4xy+15y^2=0 equation: 


Simplifying
-4x2 + 4xy + 15y2 = 0

Reorder the terms:
4xy + -4x2 + 15y2 = 0

Solving
4xy + -4x2 + 15y2 = 0

Solving for variable 'x'.

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


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

Simplifying
-2x + -3y = 0

Solving
-2x + -3y = 0

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

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

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

Divide each side by '-2'.
x = -1.5y

Simplifying
x = -1.5y

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

Simplifying
2x + -5y = 0

Solving
2x + -5y = 0

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

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

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

Divide each side by '2'.
x = 2.5y

Simplifying
x = 2.5y
Solution
x = {-1.5y, 2.5y}

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