x^2-14x*y-32y^2=0

Solution for x^2-14x*y-32y^2=0 equation:

Simplifying
x2 + -14x * y + -32y2 = 0

Multiply x * y
x2 + -14xy + -32y2 = 0

Reorder the terms:
-14xy + x2 + -32y2 = 0

Solving
-14xy + x2 + -32y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -16y)(x + 2y) = 0

Subproblem 1
Set the factor '(x + -16y)' equal to zero and attempt to solve:

Simplifying
x + -16y = 0

Solving
x + -16y = 0

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

Add '16y' to each side of the equation.
x + -16y + 16y = 0 + 16y

Combine like terms: -16y + 16y = 0
x + 0 = 0 + 16y
x = 0 + 16y
Remove the zero:
x = 16y

Simplifying
x = 16y
Subproblem 2
Set the factor '(x + 2y)' equal to zero and attempt to solve:

Simplifying
x + 2y = 0

Solving
x + 2y = 0

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

Add '-2y' to each side of the equation.
x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
x + 0 = 0 + -2y
x = 0 + -2y
Remove the zero:
x = -2y

Simplifying
x = -2y
Solution
x = {16y, -2y}