x(3+x)=-2

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

Simplifying
x(3 + x) = -2
(3 * x + x * x) = -2
(3x + x2) = -2

Solving
3x + x2 = -2

Solving for variable 'x'.

Reorder the terms:
2 + 3x + x2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 3x + x2 = 0

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

Subproblem 1
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
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 = {-2, -1}