6(2x+3)(x+1)=0

Solution for 6(2x+3)(x+1)=0 equation:

Simplifying
6(2x + 3)(x + 1) = 0

Reorder the terms:
6(3 + 2x)(x + 1) = 0

Reorder the terms:
6(3 + 2x)(1 + x) = 0

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

Combine like terms: 3x + 2x = 5x
6(3 + 5x + 2x2) = 0
(3 * 6 + 5x * 6 + 2x2 * 6) = 0
(18 + 30x + 12x2) = 0

Solving
18 + 30x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + 5x + 2x2) = 0

Factor a trinomial.
6((3 + 2x)(1 + x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

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

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

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
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 = {-1.5, -1}