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

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

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

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

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

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

Combine like terms: -2x + 2x = 0
3x(-2 + 0 + 2x2) = 0
3x(-2 + 2x2) = 0
(-2 * 3x + 2x2 * 3x) = 0
(-6x + 6x3) = 0

Solving
-6x + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-1 + x2) = 0

Factor a difference between two squares.
6x((1 + x)(-1 + x)) = 0

Ignore the factor 6.
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 '(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
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, -1, 1}