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

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

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

Reorder the terms:
3(xy + 2x2 + -3y2) = 0
(xy * 3 + 2x2 * 3 + -3y2 * 3) = 0
(3xy + 6x2 + -9y2) = 0

Solving
3xy + 6x2 + -9y2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
3((x + -1y)(2x + 3y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(x + -1y)' equal to zero and attempt to solve:

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

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

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

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

Simplifying
2x + 3y = 0

Solving
2x + 3y = 0

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

Add '-3y' to each side of the equation.
2x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
2x + 0 = 0 + -3y
2x = 0 + -3y
Remove the zero:
2x = -3y

Divide each side by '2'.
x = -1.5y

Simplifying
x = -1.5y
Solution
x = {y, -1.5y}