=x^2+xy-30y^2

Solution for =x^2+xy-30y^2 equation:

Simplifying
0 = x2 + xy + -30y2

Reorder the terms:
0 = xy + x2 + -30y2

Solving
0 = xy + x2 + -30y2

Solving for variable 'x'.
Remove the zero:
-1xy + -1x2 + 30y2 = xy + x2 + -30y2 + -1xy + -1x2 + 30y2

Reorder the terms:
-1xy + -1x2 + 30y2 = xy + -1xy + x2 + -1x2 + -30y2 + 30y2

Combine like terms: xy + -1xy = 0
-1xy + -1x2 + 30y2 = 0 + x2 + -1x2 + -30y2 + 30y2
-1xy + -1x2 + 30y2 = x2 + -1x2 + -30y2 + 30y2

Combine like terms: x2 + -1x2 = 0
-1xy + -1x2 + 30y2 = 0 + -30y2 + 30y2
-1xy + -1x2 + 30y2 = -30y2 + 30y2

Combine like terms: -30y2 + 30y2 = 0
-1xy + -1x2 + 30y2 = 0

Factor a trinomial.
(-1x + -6y)(x + -5y) = 0

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

Simplifying
-1x + -6y = 0

Solving
-1x + -6y = 0

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

Add '6y' to each side of the equation.
-1x + -6y + 6y = 0 + 6y

Combine like terms: -6y + 6y = 0
-1x + 0 = 0 + 6y
-1x = 0 + 6y
Remove the zero:
-1x = 6y

Divide each side by '-1'.
x = -6y

Simplifying
x = -6y
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 = {-6y, 5y}