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

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


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

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

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

Reorder the terms:
(3xy + 4xy + 2x2 + 6y2) = 0

Combine like terms: 3xy + 4xy = 7xy
(7xy + 2x2 + 6y2) = 0

Solving
7xy + 2x2 + 6y2 = 0

Solving for variable 'x'.

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


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

Simplifying
2x + 3y = 0

Solving
2x + 3y = 0

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

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

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

Divide each side by '2'.
x = -1.5y

Simplifying
x = -1.5y

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 = {-1.5y, -2y}

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