x^2-5x*y-50y^2=0

Solution for x^2-5x*y-50y^2=0 equation:

Simplifying
x2 + -5x * y + -50y2 = 0

Multiply x * y
x2 + -5xy + -50y2 = 0

Reorder the terms:
-5xy + x2 + -50y2 = 0

Solving
-5xy + x2 + -50y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -10y)(x + 5y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(x + 5y)' equal to zero and attempt to solve:

Simplifying
x + 5y = 0

Solving
x + 5y = 0

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

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

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

Simplifying
x = -5y
Solution
x = {10y, -5y}