=6x^2+5xy-25y^2

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Solution for =6x^2+5xy-25y^2 equation: 


Simplifying
0 = 6x2 + 5xy + -25y2

Reorder the terms:
0 = 5xy + 6x2 + -25y2

Solving
0 = 5xy + 6x2 + -25y2

Solving for variable 'x'.
Remove the zero:
-5xy + -6x2 + 25y2 = 5xy + 6x2 + -25y2 + -5xy + -6x2 + 25y2

Reorder the terms:
-5xy + -6x2 + 25y2 = 5xy + -5xy + 6x2 + -6x2 + -25y2 + 25y2

Combine like terms: 5xy + -5xy = 0
-5xy + -6x2 + 25y2 = 0 + 6x2 + -6x2 + -25y2 + 25y2
-5xy + -6x2 + 25y2 = 6x2 + -6x2 + -25y2 + 25y2

Combine like terms: 6x2 + -6x2 = 0
-5xy + -6x2 + 25y2 = 0 + -25y2 + 25y2
-5xy + -6x2 + 25y2 = -25y2 + 25y2

Combine like terms: -25y2 + 25y2 = 0
-5xy + -6x2 + 25y2 = 0

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


Subproblem 1
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

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 = {-2.5y, 1.666666667y}

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