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

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

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

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

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

Reorder the terms for easier multiplication:
x(-6 + x)(-2 + x) = 0

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

Combine like terms: -6x + -2x = -8x
x(12 + -8x + x2) = 0
(12 * x + -8x * x + x2 * x) = 0
(12x + -8x2 + x3) = 0

Solving
12x + -8x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(12 + -8x + x2) = 0

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

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 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
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, 2, 6}