(x+2y)(3x+3y)=

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Solution for (x+2y)(3x+3y)= equation: 


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

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

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

Reorder the terms:
(3xy + 6xy + 3x2 + 6y2) = 0

Combine like terms: 3xy + 6xy = 9xy
(9xy + 3x2 + 6y2) = 0

Solving
9xy + 3x2 + 6y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3xy + x2 + 2y2) = 0

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

Ignore the factor 3.

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 + 2y)' equal to zero and attempt to solve:

Simplifying
x + 2y = 0

Solving
x + 2y = 0

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

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

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

Simplifying
x = -2y
Solution
x = {-1y, -2y}

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