2(1+X)-X(3+X)=0

Solution for 2(1+X)-X(3+X)=0 equation:

Simplifying
2(1 + X) + -1X(3 + X) = 0
(1 * 2 + X * 2) + -1X(3 + X) = 0
(2 + 2X) + -1X(3 + X) = 0
2 + 2X + (3 * -1X + X * -1X) = 0
2 + 2X + (-3X + -1X2) = 0

Combine like terms: 2X + -3X = -1X
2 + -1X + -1X2 = 0

Solving
2 + -1X + -1X2 = 0

Solving for variable 'X'.

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

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

Simplifying
1 + -1X = 0

Solving
1 + -1X = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1X = 0 + -1
-1X = 0 + -1

Combine like terms: 0 + -1 = -1
-1X = -1

Divide each side by '-1'.
X = 1

Simplifying
X = 1
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 = {1, -2}