[x-6][x-3]=0

Solution for [x-6][x-3]=0 equation:

Simplifying
[x + -6][x + -3] = 0

Reorder the terms:
[-6 + x][x + -3] = 0

Reorder the terms:
[-6 + x][-3 + x] = 0

Multiply [-6 + x] * [-3 + x]
[-6[-3 + x] + x[-3 + x]] = 0
[[-3 * -6 + x * -6] + x[-3 + x]] = 0
[[18 + -6x] + x[-3 + x]] = 0
[18 + -6x + [-3 * x + x * x]] = 0
[18 + -6x + [-3x + x2]] = 0

Combine like terms: -6x + -3x = -9x
[18 + -9x + x2] = 0

Solving
18 + -9x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {3, 6}