(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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