(6x-4y)(6x-y)=0

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Solution for (6x-4y)(6x-y)=0 equation: 


Simplifying
(6x + -4y)(6x + -1y) = 0

Multiply (6x + -4y) * (6x + -1y)
(6x * (6x + -1y) + -4y * (6x + -1y)) = 0
((6x * 6x + -1y * 6x) + -4y * (6x + -1y)) = 0

Reorder the terms:
((-6xy + 36x2) + -4y * (6x + -1y)) = 0
((-6xy + 36x2) + -4y * (6x + -1y)) = 0
(-6xy + 36x2 + (6x * -4y + -1y * -4y)) = 0
(-6xy + 36x2 + (-24xy + 4y2)) = 0

Reorder the terms:
(-6xy + -24xy + 36x2 + 4y2) = 0

Combine like terms: -6xy + -24xy = -30xy
(-30xy + 36x2 + 4y2) = 0

Solving
-30xy + 36x2 + 4y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15xy + 18x2 + 2y2) = 0

Factor a trinomial.
2((3x + -2y)(6x + -1y)) = 0

Ignore the factor 2.

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

Simplifying
3x + -2y = 0

Solving
3x + -2y = 0

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

Add '2y' to each side of the equation.
3x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
3x + 0 = 0 + 2y
3x = 0 + 2y
Remove the zero:
3x = 2y

Divide each side by '3'.
x = 0.6666666667y

Simplifying
x = 0.6666666667y

Subproblem 2
Set the factor '(6x + -1y)' equal to zero and attempt to solve:

Simplifying
6x + -1y = 0

Solving
6x + -1y = 0

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

Add 'y' to each side of the equation.
6x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
6x + 0 = 0 + y
6x = 0 + y
Remove the zero:
6x = y

Divide each side by '6'.
x = 0.1666666667y

Simplifying
x = 0.1666666667y
Solution
x = {0.6666666667y, 0.1666666667y}

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