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

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


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

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

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

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

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

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

Solving for variable 'x'.
Remove the zero:
-3xy + -2x2 + 2y2 = 3xy + 2x2 + -2y2 + -3xy + -2x2 + 2y2

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

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

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

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

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


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

Simplifying
-1x + -2y = 0

Solving
-1x + -2y = 0

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

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

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

Divide each side by '-1'.
x = -2y

Simplifying
x = -2y

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

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