(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}