24(3x^2-y^2)=37xy

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Solution for 24(3x^2-y^2)=37xy equation: 


Simplifying
24(3x2 + -1y2) = 37xy
(3x2 * 24 + -1y2 * 24) = 37xy
(72x2 + -24y2) = 37xy

Solving
72x2 + -24y2 = 37xy

Solving for variable 'x'.

Reorder the terms:
-37xy + 72x2 + -24y2 = 37xy + -37xy

Combine like terms: 37xy + -37xy = 0
-37xy + 72x2 + -24y2 = 0

Factor a trinomial.
(9x + -8y)(8x + 3y) = 0


Subproblem 1
Set the factor '(9x + -8y)' equal to zero and attempt to solve:

Simplifying
9x + -8y = 0

Solving
9x + -8y = 0

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

Add '8y' to each side of the equation.
9x + -8y + 8y = 0 + 8y

Combine like terms: -8y + 8y = 0
9x + 0 = 0 + 8y
9x = 0 + 8y
Remove the zero:
9x = 8y

Divide each side by '9'.
x = 0.8888888889y

Simplifying
x = 0.8888888889y

Subproblem 2
Set the factor '(8x + 3y)' equal to zero and attempt to solve:

Simplifying
8x + 3y = 0

Solving
8x + 3y = 0

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

Add '-3y' to each side of the equation.
8x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
8x + 0 = 0 + -3y
8x = 0 + -3y
Remove the zero:
8x = -3y

Divide each side by '8'.
x = -0.375y

Simplifying
x = -0.375y
Solution
x = {0.8888888889y, -0.375y}

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