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

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

Simplifying
(3x + -6)(6 + -1x) = 0

Reorder the terms:
(-6 + 3x)(6 + -1x) = 0

Multiply (-6 + 3x) * (6 + -1x)
(-6(6 + -1x) + 3x * (6 + -1x)) = 0
((6 * -6 + -1x * -6) + 3x * (6 + -1x)) = 0
((-36 + 6x) + 3x * (6 + -1x)) = 0
(-36 + 6x + (6 * 3x + -1x * 3x)) = 0
(-36 + 6x + (18x + -3x2)) = 0

Combine like terms: 6x + 18x = 24x
(-36 + 24x + -3x2) = 0

Solving
-36 + 24x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 8x + -1x2) = 0

Factor a trinomial.
3((-6 + x)(2 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
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 = {6, 2}