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

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

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

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

Multiply (-2 + -1x) * (3 + x)
(-2(3 + x) + -1x * (3 + x)) = 0
((3 * -2 + x * -2) + -1x * (3 + x)) = 0
((-6 + -2x) + -1x * (3 + x)) = 0
(-6 + -2x + (3 * -1x + x * -1x)) = 0
(-6 + -2x + (-3x + -1x2)) = 0

Combine like terms: -2x + -3x = -5x
(-6 + -5x + -1x2) = 0

Solving
-6 + -5x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 5x + x2) = 0

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

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