x^2+14xy-15y^2=0

Solution for x^2+14xy-15y^2=0 equation:

Simplifying
x2 + 14xy + -15y2 = 0

Reorder the terms:
14xy + x2 + -15y2 = 0

Solving
14xy + x2 + -15y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -1y)(x + 15y) = 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 + 15y)' equal to zero and attempt to solve:

Simplifying
x + 15y = 0

Solving
x + 15y = 0

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

Add '-15y' to each side of the equation.
x + 15y + -15y = 0 + -15y

Combine like terms: 15y + -15y = 0
x + 0 = 0 + -15y
x = 0 + -15y
Remove the zero:
x = -15y

Simplifying
x = -15y
Solution
x = {y, -15y}