12y^2+5yx-25x^2=0

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Solution for 12y^2+5yx-25x^2=0 equation: 


Simplifying
12y2 + 5yx + -25x2 = 0

Reorder the terms:
5xy + -25x2 + 12y2 = 0

Solving
5xy + -25x2 + 12y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5x + -3y)(5x + -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 '(5x + -4y)' equal to zero and attempt to solve:

Simplifying
5x + -4y = 0

Solving
5x + -4y = 0

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

Add '4y' to each side of the equation.
5x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
5x + 0 = 0 + 4y
5x = 0 + 4y
Remove the zero:
5x = 4y

Divide each side by '5'.
x = 0.8y

Simplifying
x = 0.8y
Solution
x = {-0.6y, 0.8y}

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