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

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

Simplifying
2x2 + -3xy + 2y2 = 2(3x2 + -3xy + y2)

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

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

Add '-2y2' to each side of the equation.
-3xy + 2x2 + 2y2 + -2y2 = -6xy + 6x2 + 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-3xy + 2x2 + 0 = -6xy + 6x2 + 2y2 + -2y2
-3xy + 2x2 = -6xy + 6x2 + 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-3xy + 2x2 = -6xy + 6x2 + 0
-3xy + 2x2 = -6xy + 6x2

Solving
-3xy + 2x2 = -6xy + 6x2

Solving for variable 'x'.

Reorder the terms:
-3xy + 6xy + 2x2 + -6x2 = -6xy + 6x2 + 6xy + -6x2

Combine like terms: -3xy + 6xy = 3xy
3xy + 2x2 + -6x2 = -6xy + 6x2 + 6xy + -6x2

Combine like terms: 2x2 + -6x2 = -4x2
3xy + -4x2 = -6xy + 6x2 + 6xy + -6x2

Reorder the terms:
3xy + -4x2 = -6xy + 6xy + 6x2 + -6x2

Combine like terms: -6xy + 6xy = 0
3xy + -4x2 = 0 + 6x2 + -6x2
3xy + -4x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
3xy + -4x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(3y + -4x) = 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 '(3y + -4x)' equal to zero and attempt to solve:

Simplifying
3y + -4x = 0

Reorder the terms:
-4x + 3y = 0

Solving
-4x + 3y = 0

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

Add '-3y' to each side of the equation.
-4x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
-4x + 0 = 0 + -3y
-4x = 0 + -3y
Remove the zero:
-4x = -3y

Divide each side by '-4'.
x = 0.75y

Simplifying
x = 0.75y
Solution
x = {0, 0.75y}