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

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


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

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

Reorder the terms:
((-6xy + 9x2) + -2y * (3x + -2y)) = 0
((-6xy + 9x2) + -2y * (3x + -2y)) = 0
(-6xy + 9x2 + (3x * -2y + -2y * -2y)) = 0
(-6xy + 9x2 + (-6xy + 4y2)) = 0

Reorder the terms:
(-6xy + -6xy + 9x2 + 4y2) = 0

Combine like terms: -6xy + -6xy = -12xy
(-12xy + 9x2 + 4y2) = 0

Solving
-12xy + 9x2 + 4y2 = 0

Solving for variable 'x'.

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


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 '(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
Solution
x = {0.6666666667y, 0.6666666667y}

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