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

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

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

Reorder the terms:
x(1 + x) + 3(x + 1) = 0
(1 * x + x * x) + 3(x + 1) = 0
(1x + x2) + 3(x + 1) = 0

Reorder the terms:
1x + x2 + 3(1 + x) = 0
1x + x2 + (1 * 3 + x * 3) = 0
1x + x2 + (3 + 3x) = 0

Reorder the terms:
3 + 1x + 3x + x2 = 0

Combine like terms: 1x + 3x = 4x
3 + 4x + x2 = 0

Solving
3 + 4x + x2 = 0

Solving for variable 'x'.

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

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}