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

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

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

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

Multiply (1 + x) * (3 + -1x)
2(1(3 + -1x) + x(3 + -1x)) = 0
2((3 * 1 + -1x * 1) + x(3 + -1x)) = 0
2((3 + -1x) + x(3 + -1x)) = 0
2(3 + -1x + (3 * x + -1x * x)) = 0
2(3 + -1x + (3x + -1x2)) = 0

Combine like terms: -1x + 3x = 2x
2(3 + 2x + -1x2) = 0
(3 * 2 + 2x * 2 + -1x2 * 2) = 0
(6 + 4x + -2x2) = 0

Solving
6 + 4x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 2x + -1x2) = 0

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

Ignore the factor 2.
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 '(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 = {3, -1}