X(2x^2+3xy+y^2)=0

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Solution for X(2x^2+3xy+y^2)=0 equation: 


Simplifying
X(2x2 + 3xy + y2) = 0

Reorder the terms:
X(3xy + 2x2 + y2) = 0
(3xy * X + 2x2 * X + y2 * X) = 0
(3xyX + 2x2X + y2X) = 0

Solving
3xyX + 2x2X + y2X = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'X'.
X(3xy + 2x2 + y2) = 0

Factor a trinomial.
X((2x + y)(x + y)) = 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.

Add '-1X' to each side of the equation.
X + -1X = 0 + -1X
Remove the zero:
0 = -1X

Simplifying
0 = -1X

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
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 3
Set the factor '(x + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {-0.5y, -1y}

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