3y^2-8yx-16x^2=0

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Solution for 3y^2-8yx-16x^2=0 equation: 


Simplifying
3y2 + -8yx + -16x2 = 0

Reorder the terms:
-8xy + -16x2 + 3y2 = 0

Solving
-8xy + -16x2 + 3y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4x + -3y)(4x + -1y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4x + -1y)' equal to zero and attempt to solve:

Simplifying
4x + -1y = 0

Solving
4x + -1y = 0

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

Add 'y' to each side of the equation.
4x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
4x + 0 = 0 + y
4x = 0 + y
Remove the zero:
4x = y

Divide each side by '4'.
x = 0.25y

Simplifying
x = 0.25y
Solution
x = {-0.75y, 0.25y}

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