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

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


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

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

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

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

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

Solving
1xy + x2 + -2y2 = 0

Solving for variable 'x'.

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


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

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

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

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

Simplifying
x = y

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 = {y, -2y}

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