3x^2-16xy+21y^2=0

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Solution for 3x^2-16xy+21y^2=0 equation: 


Simplifying
3x2 + -16xy + 21y2 = 0

Reorder the terms:
-16xy + 3x2 + 21y2 = 0

Solving
-16xy + 3x2 + 21y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -3y)(3x + -7y) = 0


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

Simplifying
x + -3y = 0

Solving
x + -3y = 0

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

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

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

Simplifying
x = 3y

Subproblem 2
Set the factor '(3x + -7y)' equal to zero and attempt to solve:

Simplifying
3x + -7y = 0

Solving
3x + -7y = 0

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

Add '7y' to each side of the equation.
3x + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
3x + 0 = 0 + 7y
3x = 0 + 7y
Remove the zero:
3x = 7y

Divide each side by '3'.
x = 2.333333333y

Simplifying
x = 2.333333333y
Solution
x = {3y, 2.333333333y}

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