x^2+14xy+24y^2=0

Solution for x^2+14xy+24y^2=0 equation:

Simplifying
x2 + 14xy + 24y2 = 0

Reorder the terms:
14xy + x2 + 24y2 = 0

Solving
14xy + x2 + 24y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + 2y)(x + 12y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(x + 12y)' equal to zero and attempt to solve:

Simplifying
x + 12y = 0

Solving
x + 12y = 0

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

Add '-12y' to each side of the equation.
x + 12y + -12y = 0 + -12y

Combine like terms: 12y + -12y = 0
x + 0 = 0 + -12y
x = 0 + -12y
Remove the zero:
x = -12y

Simplifying
x = -12y
Solution
x = {-2y, -12y}