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

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


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

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

Reorder the terms:
((-18xy + 42x2) + -7y * (7x + -3y)) = 0
((-18xy + 42x2) + -7y * (7x + -3y)) = 0
(-18xy + 42x2 + (7x * -7y + -3y * -7y)) = 0
(-18xy + 42x2 + (-49xy + 21y2)) = 0

Reorder the terms:
(-18xy + -49xy + 42x2 + 21y2) = 0

Combine like terms: -18xy + -49xy = -67xy
(-67xy + 42x2 + 21y2) = 0

Solving
-67xy + 42x2 + 21y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6x + -7y)(7x + -3y) = 0


Subproblem 1
Set the factor '(6x + -7y)' equal to zero and attempt to solve:

Simplifying
6x + -7y = 0

Solving
6x + -7y = 0

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

Add '7y' to each side of the equation.
6x + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
6x + 0 = 0 + 7y
6x = 0 + 7y
Remove the zero:
6x = 7y

Divide each side by '6'.
x = 1.166666667y

Simplifying
x = 1.166666667y

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

Simplifying
7x + -3y = 0

Solving
7x + -3y = 0

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

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

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

Divide each side by '7'.
x = 0.4285714286y

Simplifying
x = 0.4285714286y
Solution
x = {1.166666667y, 0.4285714286y}

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