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

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


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

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

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

Reorder the terms:
(-9xy + 2xy + 6x2 + -3y2) = 0

Combine like terms: -9xy + 2xy = -7xy
(-7xy + 6x2 + -3y2) = 0

Solving
-7xy + 6x2 + -3y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2x + -3y)(3x + y) = 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 '(3x + y)' equal to zero and attempt to solve:

Simplifying
3x + y = 0

Solving
3x + y = 0

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

Add '-1y' to each side of the equation.
3x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
3x + 0 = 0 + -1y
3x = 0 + -1y
Remove the zero:
3x = -1y

Divide each side by '3'.
x = -0.3333333333y

Simplifying
x = -0.3333333333y
Solution
x = {1.5y, -0.3333333333y}

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