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

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

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

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

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

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

Combine like terms: -2x + -6x = -8x
3(12 + -8x + x2) = 0
(12 * 3 + -8x * 3 + x2 * 3) = 0
(36 + -24x + 3x2) = 0

Solving
36 + -24x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -8x + x2) = 0

Factor a trinomial.
3((2 + -1x)(6 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
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 2
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 = {2, 6}