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

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

Simplifying
2x2 + 14xy + 24y2 = 0

Reorder the terms:
14xy + 2x2 + 24y2 = 0

Solving
14xy + 2x2 + 24y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7xy + x2 + 12y2) = 0

Factor a trinomial.
2((x + 3y)(x + 4y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(x + 3y)' equal to zero and attempt to solve:

Simplifying
x + 3y = 0

Solving
x + 3y = 0

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

Add '-3y' to each side of the equation.
x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
x + 0 = 0 + -3y
x = 0 + -3y
Remove the zero:
x = -3y

Simplifying
x = -3y
Subproblem 2
Set the factor '(x + 4y)' equal to zero and attempt to solve:

Simplifying
x + 4y = 0

Solving
x + 4y = 0

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

Add '-4y' to each side of the equation.
x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
x + 0 = 0 + -4y
x = 0 + -4y
Remove the zero:
x = -4y

Simplifying
x = -4y
Solution
x = {-3y, -4y}