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

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

Simplifying
3(x + 2) + -1x(x + 2) = 0

Reorder the terms:
3(2 + x) + -1x(x + 2) = 0
(2 * 3 + x * 3) + -1x(x + 2) = 0
(6 + 3x) + -1x(x + 2) = 0

Reorder the terms:
6 + 3x + -1x(2 + x) = 0
6 + 3x + (2 * -1x + x * -1x) = 0
6 + 3x + (-2x + -1x2) = 0

Combine like terms: 3x + -2x = 1x
6 + 1x + -1x2 = 0

Solving
6 + 1x + -1x2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {3, -2}