5x^2-xy-6y^2=0

Solution for 5x^2-xy-6y^2=0 equation:

Simplifying
5x2 + -1xy + -6y2 = 0

Reorder the terms:
-1xy + 5x2 + -6y2 = 0

Solving
-1xy + 5x2 + -6y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + -6y)(x + y) = 0

Subproblem 1
Set the factor '(5x + -6y)' equal to zero and attempt to solve:

Simplifying
5x + -6y = 0

Solving
5x + -6y = 0

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

Add '6y' to each side of the equation.
5x + -6y + 6y = 0 + 6y

Combine like terms: -6y + 6y = 0
5x + 0 = 0 + 6y
5x = 0 + 6y
Remove the zero:
5x = 6y

Divide each side by '5'.
x = 1.2y

Simplifying
x = 1.2y
Subproblem 2
Set the factor '(x + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {1.2y, -1y}