24x^2+2xy-12y^2=

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Solution for 24x^2+2xy-12y^2= equation: 


Simplifying
24x2 + 2xy + -12y2 = 0

Reorder the terms:
2xy + 24x2 + -12y2 = 0

Solving
2xy + 24x2 + -12y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(xy + 12x2 + -6y2) = 0

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

Ignore the factor 2.

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

Simplifying
3x + -2y = 0

Solving
3x + -2y = 0

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

Add '2y' to each side of the equation.
3x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
3x + 0 = 0 + 2y
3x = 0 + 2y
Remove the zero:
3x = 2y

Divide each side by '3'.
x = 0.6666666667y

Simplifying
x = 0.6666666667y

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

Simplifying
4x + 3y = 0

Solving
4x + 3y = 0

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

Add '-3y' to each side of the equation.
4x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
4x + 0 = 0 + -3y
4x = 0 + -3y
Remove the zero:
4x = -3y

Divide each side by '4'.
x = -0.75y

Simplifying
x = -0.75y
Solution
x = {0.6666666667y, -0.75y}

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