3x+x(3-2x)=0

Solution for 3x+x(3-2x)=0 equation:

Simplifying
3x + x(3 + -2x) = 0
3x + (3 * x + -2x * x) = 0
3x + (3x + -2x2) = 0

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

Solving
6x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(3 + -1x) = 0

Ignore the factor 2.
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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, 3}