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

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


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

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

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

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

Combine like terms: 9xy + 4xy = 13xy
(13xy + 6x2 + 6y2) = 0

Solving
13xy + 6x2 + 6y2 = 0

Solving for variable 'x'.

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

Solution

x = {-0.6666666667y, -1.5y}

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