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

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

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

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

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

Multiply (-3 + x) * (-6 + 3x)
(-3(-6 + 3x) + x(-6 + 3x)) = 0
((-6 * -3 + 3x * -3) + x(-6 + 3x)) = 0
((18 + -9x) + x(-6 + 3x)) = 0
(18 + -9x + (-6 * x + 3x * x)) = 0
(18 + -9x + (-6x + 3x2)) = 0

Combine like terms: -9x + -6x = -15x
(18 + -15x + 3x2) = 0

Solving
18 + -15x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + -5x + x2) = 0

Factor a trinomial.
3((2 + -1x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {2, 3}