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

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

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

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

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

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

Combine like terms: -3x + -6x = -9x
(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}