(6x-2y)(3x-7y)=0

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Solution for (6x-2y)(3x-7y)=0 equation: 


Simplifying
(6x + -2y)(3x + -7y) = 0

Multiply (6x + -2y) * (3x + -7y)
(6x * (3x + -7y) + -2y * (3x + -7y)) = 0
((3x * 6x + -7y * 6x) + -2y * (3x + -7y)) = 0

Reorder the terms:
((-42xy + 18x2) + -2y * (3x + -7y)) = 0
((-42xy + 18x2) + -2y * (3x + -7y)) = 0
(-42xy + 18x2 + (3x * -2y + -7y * -2y)) = 0
(-42xy + 18x2 + (-6xy + 14y2)) = 0

Reorder the terms:
(-42xy + -6xy + 18x2 + 14y2) = 0

Combine like terms: -42xy + -6xy = -48xy
(-48xy + 18x2 + 14y2) = 0

Solving
-48xy + 18x2 + 14y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24xy + 9x2 + 7y2) = 0

Factor a trinomial.
2((3x + -7y)(3x + -1y)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(3x + -1y)' equal to zero and attempt to solve:

Simplifying
3x + -1y = 0

Solving
3x + -1y = 0

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

Add 'y' to each side of the equation.
3x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
3x + 0 = 0 + y
3x = 0 + y
Remove the zero:
3x = y

Divide each side by '3'.
x = 0.3333333333y

Simplifying
x = 0.3333333333y
Solution
x = {2.333333333y, 0.3333333333y}

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