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

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


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

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

Reorder the terms:
((-1xy + 2x2) + 2y * (2x + -1y)) = 0
((-1xy + 2x2) + 2y * (2x + -1y)) = 0
(-1xy + 2x2 + (2x * 2y + -1y * 2y)) = 0
(-1xy + 2x2 + (4xy + -2y2)) = 0

Reorder the terms:
(-1xy + 4xy + 2x2 + -2y2) = 0

Combine like terms: -1xy + 4xy = 3xy
(3xy + 2x2 + -2y2) = 0

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

Solving for variable 'x'.

Factor a trinomial.
(2x + -1y)(x + 2y) = 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 + 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
Solution
x = {0.5y, -2y}

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