5x^2+23xy+12y^2=0

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Solution for 5x^2+23xy+12y^2=0 equation: 


Simplifying
5x2 + 23xy + 12y2 = 0

Reorder the terms:
23xy + 5x2 + 12y2 = 0

Solving
23xy + 5x2 + 12y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + 3y)(x + 4y) = 0


Subproblem 1
Set the factor '(5x + 3y)' equal to zero and attempt to solve:

Simplifying
5x + 3y = 0

Solving
5x + 3y = 0

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

Add '-3y' to each side of the equation.
5x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
5x + 0 = 0 + -3y
5x = 0 + -3y
Remove the zero:
5x = -3y

Divide each side by '5'.
x = -0.6y

Simplifying
x = -0.6y

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 = {-0.6y, -4y}

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