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

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


Simplifying
(3y + -1x)(2x + y) = 0

Reorder the terms:
(-1x + 3y)(2x + y) = 0

Multiply (-1x + 3y) * (2x + y)
(-1x * (2x + y) + 3y * (2x + y)) = 0
((2x * -1x + y * -1x) + 3y * (2x + y)) = 0

Reorder the terms:
((-1xy + -2x2) + 3y * (2x + y)) = 0
((-1xy + -2x2) + 3y * (2x + y)) = 0
(-1xy + -2x2 + (2x * 3y + y * 3y)) = 0
(-1xy + -2x2 + (6xy + 3y2)) = 0

Reorder the terms:
(-1xy + 6xy + -2x2 + 3y2) = 0

Combine like terms: -1xy + 6xy = 5xy
(5xy + -2x2 + 3y2) = 0

Solving
5xy + -2x2 + 3y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2x + -1y)(x + -3y) = 0


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

Simplifying
-2x + -1y = 0

Solving
-2x + -1y = 0

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

Add 'y' to each side of the equation.
-2x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
-2x + 0 = 0 + y
-2x = 0 + y
Remove the zero:
-2x = y

Divide each side by '-2'.
x = -0.5y

Simplifying
x = -0.5y

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

Simplifying
x + -3y = 0

Solving
x + -3y = 0

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

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

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

Simplifying
x = 3y
Solution
x = {-0.5y, 3y}

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