6xy+90x^2-12y^2=0

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Solution for 6xy+90x^2-12y^2=0 equation: 


Simplifying
6xy + 90x2 + -12y2 = 0

Solving
6xy + 90x2 + -12y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(xy + 15x2 + -2y2) = 0

Factor a trinomial.
6((3x + -1y)(5x + 2y)) = 0

Ignore the factor 6.

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

Simplifying
3x + -1y = 0

Solving
3x + -1y = 0

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

Add 'y' to each side of the equation.
3x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
3x + 0 = 0 + y
3x = 0 + y
Remove the zero:
3x = y

Divide each side by '3'.
x = 0.3333333333y

Simplifying
x = 0.3333333333y

Subproblem 2
Set the factor '(5x + 2y)' equal to zero and attempt to solve:

Simplifying
5x + 2y = 0

Solving
5x + 2y = 0

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

Add '-2y' to each side of the equation.
5x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
5x + 0 = 0 + -2y
5x = 0 + -2y
Remove the zero:
5x = -2y

Divide each side by '5'.
x = -0.4y

Simplifying
x = -0.4y
Solution
x = {0.3333333333y, -0.4y}

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