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

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

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

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

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

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

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

Solving
-2 + -4x + -2x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor -2.
Subproblem 1
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
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 = {-1, -1}