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

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


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

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

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

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

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

Multiply (3x + y) * (3x + y)
-1xy + 2x2 + -1y2 + (3x * (3x + y) + y(3x + y)) = 0
-1xy + 2x2 + -1y2 + ((3x * 3x + y * 3x) + y(3x + y)) = 0

Reorder the terms:
-1xy + 2x2 + -1y2 + ((3xy + 9x2) + y(3x + y)) = 0
-1xy + 2x2 + -1y2 + ((3xy + 9x2) + y(3x + y)) = 0
-1xy + 2x2 + -1y2 + (3xy + 9x2 + (3x * y + y * y)) = 0
-1xy + 2x2 + -1y2 + (3xy + 9x2 + (3xy + y2)) = 0

Reorder the terms:
-1xy + 2x2 + -1y2 + (3xy + 3xy + 9x2 + y2) = 0

Combine like terms: 3xy + 3xy = 6xy
-1xy + 2x2 + -1y2 + (6xy + 9x2 + y2) = 0

Reorder the terms:
-1xy + 6xy + 2x2 + 9x2 + -1y2 + y2 = 0

Combine like terms: -1xy + 6xy = 5xy
5xy + 2x2 + 9x2 + -1y2 + y2 = 0

Combine like terms: 2x2 + 9x2 = 11x2
5xy + 11x2 + -1y2 + y2 = 0

Combine like terms: -1y2 + y2 = 0
5xy + 11x2 + 0 = 0
5xy + 11x2 = 0

Solving
5xy + 11x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(5y + 11x) = 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 '(5y + 11x)' equal to zero and attempt to solve:

Simplifying
5y + 11x = 0

Reorder the terms:
11x + 5y = 0

Solving
11x + 5y = 0

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

Add '-5y' to each side of the equation.
11x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
11x + 0 = 0 + -5y
11x = 0 + -5y
Remove the zero:
11x = -5y

Divide each side by '11'.
x = -0.4545454545y

Simplifying
x = -0.4545454545y
Solution
x = {0, -0.4545454545y}

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