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

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

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

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

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

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

Solving
6 + -1x + -1x2 = 0

Solving for variable 'x'.

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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

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

Simplifying
3 + x = 0

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

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

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

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