((x-2x)+2x(y+10xy))=0

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Solution for ((x-2x)+2x(y+10xy))=0 equation: 


Simplifying
((x + -2x) + 2x(y + 10xy)) = 0

Combine like terms: x + -2x = -1x
((-1x) + 2x(y + 10xy)) = 0
((-1x) + 2x(y + 10xy)) = 0

Reorder the terms:
((-1x) + 2x(10xy + y)) = 0
((-1x) + (10xy * 2x + y * 2x)) = 0

Reorder the terms:
((-1x) + (2xy + 20x2y)) = 0
((-1x) + (2xy + 20x2y)) = 0

Remove parenthesis around ((-1x) + 2xy + 20x2y)
(-1x) + 2xy + 20x2y = 0

Solving
(-1x) + 2xy + 20x2y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + 2y + 20xy) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-1 + 2y + 20xy)' equal to zero and attempt to solve:

Simplifying
-1 + 2y + 20xy = 0

Reorder the terms:
-1 + 20xy + 2y = 0

Solving
-1 + 20xy + 2y = 0

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

Add '1' to each side of the equation.
-1 + 20xy + 1 + 2y = 0 + 1

Reorder the terms:
-1 + 1 + 20xy + 2y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 20xy + 2y = 0 + 1
20xy + 2y = 0 + 1

Combine like terms: 0 + 1 = 1
20xy + 2y = 1

Add '-2y' to each side of the equation.
20xy + 2y + -2y = 1 + -2y

Combine like terms: 2y + -2y = 0
20xy + 0 = 1 + -2y
20xy = 1 + -2y

Divide each side by '20y'.
x = 0.05y-1 + -0.1

Simplifying
x = 0.05y-1 + -0.1

Reorder the terms:
x = -0.1 + 0.05y-1
Solution
x = {0, -0.1 + 0.05y-1}

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