10x^2-4xy-6y^2=0

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Solution for 10x^2-4xy-6y^2=0 equation: 


Simplifying
10x2 + -4xy + -6y2 = 0

Reorder the terms:
-4xy + 10x2 + -6y2 = 0

Solving
-4xy + 10x2 + -6y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2xy + 5x2 + -3y2) = 0

Factor a trinomial.
2((x + -1y)(5x + 3y)) = 0

Ignore the factor 2.

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

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

Add 'y' to each side of the equation.
x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
x + 0 = 0 + y
x = 0 + y
Remove the zero:
x = y

Simplifying
x = y

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 = {y, -0.6y}

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