-x(2x-y)-2y(y+3x)=

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Solution for -x(2x-y)-2y(y+3x)= equation: 


Simplifying
-1x(2x + -1y) + -2y(y + 3x) = 0
(2x * -1x + -1y * -1x) + -2y(y + 3x) = 0

Reorder the terms:
(1xy + -2x2) + -2y(y + 3x) = 0
(1xy + -2x2) + -2y(y + 3x) = 0

Reorder the terms:
1xy + -2x2 + -2y(3x + y) = 0
1xy + -2x2 + (3x * -2y + y * -2y) = 0
1xy + -2x2 + (-6xy + -2y2) = 0

Reorder the terms:
1xy + -6xy + -2x2 + -2y2 = 0

Combine like terms: 1xy + -6xy = -5xy
-5xy + -2x2 + -2y2 = 0

Solving
-5xy + -2x2 + -2y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5xy + 2x2 + 2y2) = 0

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

Ignore the factor -1.

Subproblem 1
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

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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