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

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


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

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

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

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

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

Solving
-1xy + 2x2 + -3y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2x + -3y)(x + 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 '(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
Solution
x = {1.5y, -1y}

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