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

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

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

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

Reorder the terms:
-6xy + 3x2 + 2xy(3 + x) = 0
-6xy + 3x2 + (3 * 2xy + x * 2xy) = 0
-6xy + 3x2 + (6xy + 2x2y) = 0

Reorder the terms:
-6xy + 6xy + 3x2 + 2x2y = 0

Combine like terms: -6xy + 6xy = 0
0 + 3x2 + 2x2y = 0
3x2 + 2x2y = 0

Solving
3x2 + 2x2y = 0

Solving for variable 'x'.

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

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

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(3 + 2y)' equal to zero and attempt to solve:

Simplifying
3 + 2y = 0

Solving
3 + 2y = 0

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

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

Combine like terms: 3 + -3 = 0
0 + 2y = 0 + -3
2y = 0 + -3

Combine like terms: 0 + -3 = -3
2y = -3

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

Combine like terms: 2y + -2y = 0
0 = -3 + -2y

Simplifying
0 = -3 + -2y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}