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

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

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

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

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

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

Combine like terms: 6x + 3x = 9x
0 = x(6 + 9x + 3x2)
0 = (6 * x + 9x * x + 3x2 * x)
0 = (6x + 9x2 + 3x3)

Solving
0 = 6x + 9x2 + 3x3

Solving for variable 'x'.
Remove the zero:
-6x + -9x2 + -3x3 = 6x + 9x2 + 3x3 + -6x + -9x2 + -3x3

Reorder the terms:
-6x + -9x2 + -3x3 = 6x + -6x + 9x2 + -9x2 + 3x3 + -3x3

Combine like terms: 6x + -6x = 0
-6x + -9x2 + -3x3 = 0 + 9x2 + -9x2 + 3x3 + -3x3
-6x + -9x2 + -3x3 = 9x2 + -9x2 + 3x3 + -3x3

Combine like terms: 9x2 + -9x2 = 0
-6x + -9x2 + -3x3 = 0 + 3x3 + -3x3
-6x + -9x2 + -3x3 = 3x3 + -3x3

Combine like terms: 3x3 + -3x3 = 0
-6x + -9x2 + -3x3 = 0

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

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

Ignore the factor -3.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0
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
Subproblem 3
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 = {0, -2, -1}