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

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

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

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

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

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

Combine like terms: -2x + -1x = -3x
3(2 + -3x + x2) = 0
(2 * 3 + -3x * 3 + x2 * 3) = 0
(6 + -9x + 3x2) = 0

Solving
6 + -9x + 3x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
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
Solution
x = {1, 2}