(3x+6)(x+1)=0

Solution for (3x+6)(x+1)=0 equation:

Simplifying
(3x + 6)(x + 1) = 0

Reorder the terms:
(6 + 3x)(x + 1) = 0

Reorder the terms:
(6 + 3x)(1 + x) = 0

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

Combine like terms: 6x + 3x = 9x
(6 + 9x + 3x2) = 0

Solving
6 + 9x + 3x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 3.
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}