x^2+9xy-10y^2=0

Solution for x^2+9xy-10y^2=0 equation:

Simplifying
x2 + 9xy + -10y2 = 0

Reorder the terms:
9xy + x2 + -10y2 = 0

Solving
9xy + x2 + -10y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -1y)(x + 10y) = 0

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 '(x + 10y)' equal to zero and attempt to solve:

Simplifying
x + 10y = 0

Solving
x + 10y = 0

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

Add '-10y' to each side of the equation.
x + 10y + -10y = 0 + -10y

Combine like terms: 10y + -10y = 0
x + 0 = 0 + -10y
x = 0 + -10y
Remove the zero:
x = -10y

Simplifying
x = -10y
Solution
x = {y, -10y}