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

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


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

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

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

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

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

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

Solving for variable 'x'.

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


Subproblem 1
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

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

Simplifying
2x + y = 0

Solving
2x + y = 0

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

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

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

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

Simplifying
x = -0.5y
Solution
x = {2y, -0.5y}

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