(3x+3y)(3x+3y)=0

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Solution for (3x+3y)(3x+3y)=0 equation: 


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

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

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

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

Combine like terms: 9xy + 9xy = 18xy
(18xy + 9x2 + 9y2) = 0

Solving
18xy + 9x2 + 9y2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
9((x + y)(x + y)) = 0

Ignore the factor 9.

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {-1y, -1y}

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