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

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

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

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

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

Multiply (-6 + x) * (2 + 3x)
2x(-6(2 + 3x) + x(2 + 3x)) = 0
2x((2 * -6 + 3x * -6) + x(2 + 3x)) = 0
2x((-12 + -18x) + x(2 + 3x)) = 0
2x(-12 + -18x + (2 * x + 3x * x)) = 0
2x(-12 + -18x + (2x + 3x2)) = 0

Combine like terms: -18x + 2x = -16x
2x(-12 + -16x + 3x2) = 0
(-12 * 2x + -16x * 2x + 3x2 * 2x) = 0
(-24x + -32x2 + 6x3) = 0

Solving
-24x + -32x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-12 + -16x + 3x2) = 0

Factor a trinomial.
2x((-2 + -3x)(6 + -1x)) = 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 '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

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

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

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

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, -0.6666666667, 6}