=x^2-xy-42y^2

Solution for =x^2-xy-42y^2 equation:

Simplifying
0 = x2 + -1xy + -42y2

Reorder the terms:
0 = -1xy + x2 + -42y2

Solving
0 = -1xy + x2 + -42y2

Solving for variable 'x'.
Remove the zero:
xy + -1x2 + 42y2 = -1xy + x2 + -42y2 + xy + -1x2 + 42y2

Reorder the terms:
xy + -1x2 + 42y2 = -1xy + xy + x2 + -1x2 + -42y2 + 42y2

Combine like terms: -1xy + xy = 0
xy + -1x2 + 42y2 = 0 + x2 + -1x2 + -42y2 + 42y2
xy + -1x2 + 42y2 = x2 + -1x2 + -42y2 + 42y2

Combine like terms: x2 + -1x2 = 0
xy + -1x2 + 42y2 = 0 + -42y2 + 42y2
xy + -1x2 + 42y2 = -42y2 + 42y2

Combine like terms: -42y2 + 42y2 = 0
xy + -1x2 + 42y2 = 0

Factor a trinomial.
(-1x + -6y)(x + -7y) = 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 + -7y)' equal to zero and attempt to solve:

Simplifying
x + -7y = 0

Solving
x + -7y = 0

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

Add '7y' to each side of the equation.
x + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
x + 0 = 0 + 7y
x = 0 + 7y
Remove the zero:
x = 7y

Simplifying
x = 7y
Solution
x = {-6y, 7y}