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

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

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

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

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

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

Combine like terms: -6x + -2x = -8x
x(-6 + -8x + -2x2) = 0
(-6 * x + -8x * x + -2x2 * x) = 0
(-6x + -8x2 + -2x3) = 0

Solving
-6x + -8x2 + -2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-2x'.
-2x(3 + 4x + x2) = 0

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

Ignore the factor -2.
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 '(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 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, -3, -1}