5x^2-7xy-12y^2=0

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Solution for 5x^2-7xy-12y^2=0 equation: 


Simplifying
5x2 + -7xy + -12y2 = 0

Reorder the terms:
-7xy + 5x2 + -12y2 = 0

Solving
-7xy + 5x2 + -12y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + -12y)(x + y) = 0


Subproblem 1
Set the factor '(5x + -12y)' equal to zero and attempt to solve:

Simplifying
5x + -12y = 0

Solving
5x + -12y = 0

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

Add '12y' to each side of the equation.
5x + -12y + 12y = 0 + 12y

Combine like terms: -12y + 12y = 0
5x + 0 = 0 + 12y
5x = 0 + 12y
Remove the zero:
5x = 12y

Divide each side by '5'.
x = 2.4y

Simplifying
x = 2.4y

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {2.4y, -1y}

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