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

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

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

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

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

Reorder the terms for easier multiplication:
3 * 2(-1 + x)(-2 + x) = 0

Multiply 3 * 2
6(-1 + x)(-2 + x) = 0

Multiply (-1 + x) * (-2 + x)
6(-1(-2 + x) + x(-2 + x)) = 0
6((-2 * -1 + x * -1) + x(-2 + x)) = 0
6((2 + -1x) + x(-2 + x)) = 0
6(2 + -1x + (-2 * x + x * x)) = 0
6(2 + -1x + (-2x + x2)) = 0

Combine like terms: -1x + -2x = -3x
6(2 + -3x + x2) = 0
(2 * 6 + -3x * 6 + x2 * 6) = 0
(12 + -18x + 6x2) = 0

Solving
12 + -18x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(2 + -3x + x2) = 0

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

Ignore the factor 6.
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}