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

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

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

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

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

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

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