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

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

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

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

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

Add '-2' to each side of the equation.
2 + -1X + -2 + -1X2 = 2 + -2

Reorder the terms:
2 + -2 + -1X + -1X2 = 2 + -2

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

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

Solving
-1X + -1X2 = 0

Solving for variable 'X'.

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

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

Simplifying
1 + X = 0

Solving
1 + X = 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 + X = 0 + -1

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

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

Simplifying
X = -1
Solution
X = {0, -1}