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

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

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

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

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

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

Combine like terms: 1x + 3x = 4x
-2(3 + 4x + x2) = 0
(3 * -2 + 4x * -2 + x2 * -2) = 0
(-6 + -8x + -2x2) = 0

Solving
-6 + -8x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 4x + x2) = 0

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

Ignore the factor -2.
Subproblem 1
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
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}